Publications
2025
| arxiv |
Topology, Kinetics and Inheritance in Clonal Colonies of Bone Marrow Stromal Cells |
| A. Allegrezza, R. Beschi, D. Caudo, A.Cavagna, A. Corsi, A. Culla, S. Donsante, G. Giannicola, I. Giardina, G. Gosti, T.S. Grigera, S. Melillo, B. Palmisano, L. Parisi, L. Postiglione, M. Riminucci, F.S. Rotondi |
| Bone marrow stromal cells (BMSCs), whose populations contain multipotent skeletal stem cells with relevant therapeutic applications, are known to produce very heterogeneous colonies upon in vitro culture, a trait that may severely hinder the clinical usefulness of BMSC-based therapies. Therefore, reaching a better insight on the nature of such heterogeneity, as well as on the factors determining it, is important. Here, by using time-lapse microscopy, we study the structure of N=28 human BMSC colonies from six donors, each colony derived from a single cell, and trace their lineage trees up to the seventh generation. We confirm the presence of very significant inter-colony and intra-colony heterogeneities, both in the topology of the lineages and in the replicative kinetics of the colonies. We also find that topology and kinetics are strongly correlated, consistent with the existence of regulating factors linking the sub-population of inactive cells, which uniquely determine a lineage’s topology, and that of active cells, which are the sole responsible for the proliferation rate of the colony. Finally, we submit each colony to an entropy-based inheritance test, which measures the degree of non-random clustering of inactive cells within the same branches of the lineage, and find a clear signature of hereditary transmission of the probability of emergence of inactive cells in the largest majority of the experimental lineages. |
| https://doi.org/10.48550/arXiv.2504.21818 |
| Journal of Physics: Condensed Matter |
The 2025 motile active matter roadmap |
| G. Gompper et al. |
| Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area. |
| https://iopscience.iop.org/article/10.1088/1361-648X/adac98 |
| New Journal of Physics |
Conceptual and practical approaches for investigating irreversible processes |
| D. Lucente, M. Baldovin, F. Cecconi, M. Cencini, N. Cocciaglia, A. Puglisi, M. Viale, A. Vulpiani |
| Current research in statistical mechanics mostly concerns the investigation of out-of-equilibrium, irreversible processes, which are ubiquitous in nature and still far from being theoretically understood. Even the precise characterization of irreversibility is the object of an open debate: while in the context of Hamiltonian systems the one-century-old proposal by M. Smoluchowski looks still valid (a process appears irreversible when the initial state has a recurrence time that is long compared to the time of observation (Smoluchowski 1916 Z. Phys. 17 557–85)), in dissipative systems, particularly in the case of stochastic processes, the problem is more involved, and quantifying the ‘degree of irreversibility’ is a pragmatic need. The most employed strategies rely on the estimation of entropy production: this quantity, although mathematically well-defined, is often difficult to compute, especially when analyzing experimental data. Moreover, being a global observable, entropy production fails to capture specific aspects of irreversibility in extended systems, such as the role of different currents and their spatial development. This review aims to address various conceptual and technical challenges encountered in the analysis of irreversibility, including the role of the coarse-graining procedure and the treatment of data in the absence of complete information. The discussion will be mostly based on simple models, analytically treatable, and supplemented by examples of complex, more realistic non-equilibrium systems. |
| https://iopscience.iop.org/article/10.1088/1367-2630/adc6ab |
| Journal of Statistical Mechanics: Theory and Experiment |
H-theorem at negative temperature: the random exchange model with bounds |
| D. Lucente, M. Baldovin, A. Puglisi, A. Vulpiani |
| Random exchange kinetic models are widely employed to describe the conservative dynamics of large interacting systems. Due to their simplicity and generality, they are quite popular in several fields, from statistical mechanics to biophysics and economics. Here, we study a version where bounds on the individual shares of a globally conserved quantity are introduced. We analytically show that this dynamic allows stationary states with population inversion, described by Boltzmann statistics at negative absolute temperature, if the conserved quantity has the physical meaning of an energy. The proposed model therefore provides a privileged system for the study of thermalization towards a negative temperature state. First, the genuine equilibrium nature of the stationary state is verified by checking the detailed balance condition. Then, an H-theorem is proven, ensuring that such equilibrium condition is reached by a monotonic increase in the Boltzmann entropy. We also provide analytical and numerical evidence that a large intruder in contact with the system thermalizes, suggesting a practical way to design a thermal bath at negative temperature. |
| https://iopscience.iop.org/article/10.1088/1742-5468/ada49b |
| Physical Review E |
Minimal work protocols for inertial particles in nonharmonic traps |
| J. Sanders, M. Baldovin, P. Muratore-Ginanneschi |
| Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a time-dependent potential applied to a nanoparticle to reach a target stationary state in a given time with minimal energy cost. We study this problem for a particle subject to thermal fluctuations in a regime that takes into account the effects of inertia, and, building on the results of a previous work, we provide a numerical method to find optimal controls even for non-Gaussian initial and final conditions, corresponding to nonharmonic confinements. Although we focus on a regime where the driving time is long compared to the characteristic relaxation times of the dynamics, the control protocol and the time-dependent position distribution are qualitatively different from the corresponding overdamped limit: in particular, a symmetry of the boundary conditions, which is preserved in the absence of inertia, turns out to be broken in the underdamped regime. We also show that the momentum mean tends to a constant value along the trajectory, except close to the boundary, while the evolution of the position mean and of the second moments is highly nontrivial. Our results also support that the lower bound on the optimal entropy production computed from the overdamped case is tight in the adiabatic limit. |
| https://doi.org/10.1103/PhysRevE.111.034127 |
| Entropy |
Optimal Control of an Electromechanical Energy Harvester |
| D. Lucente, A. Manacorda, A. Plati, A. Sarracino, M. Baldovin |
| Many techniques originally developed in the context of deterministic control theory have recently been applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable parameters in time in order to maximize, on average, a certain reward function, while steering the system between two pre-assigned states. In this work, we study the problem of optimal control for a wide class of stochastic systems, inspired by a model of an energy harvester. The stochastic noise in this system is due to the mechanical vibrations, while the reward function is the average power extracted from them. We consider the case in which the electrical resistance of the harvester can be changed in time, and we exploit the tools of control theory to work out optimal solutions in a perturbative regime, close to the stationary state. Our results show that it is possible to design protocols that perform better than any possible solution with constant resistance. |
| https://www.mdpi.com/1099-4300/27/3/268 |
| European Journal of Mechanics-A/Solids |
Control of friction: Shortcuts and optimization for the rate-and state-variable equation |
| A. Plati, A. Petri, M. Baldovin |
| Frictional forces are a key ingredient of any physical description of the macroscopic world, as they account for the phenomena causing transformation of mechanical energy into heat. They are ubiquitous in nature, and a wide range of practical applications involve the manipulation of physical systems where friction plays a crucial role. In this paper, we apply control theory to dynamics governed by the paradigmatic rate- and state-variable law for solid-on-solid friction. Several control problems are considered for the case of a slider dragged on a surface by an elastic spring. By using swift state-to-state protocols, we show how to drive the system between two arbitrary stationary states characterized by different constant sliding velocities in a given time. Remarkably, this task proves to be feasible even when specific constraints are imposed on the dynamics, such as preventing the instantaneous sliding velocity or the frictional force from exceeding a prescribed bound. The derived driving protocols also allow to avoid a stick–slip instability, which instead occurs when velocity is suddenly switched. By exploiting variational methods, we also address the functional minimization problem of finding the optimal protocol that connects two steady states in a specified time, while minimizing the work done by the friction. We find that the optimal strategy can change qualitatively depending on the time imposed for the duration of the process. The validity of the proposed protocols in real situations depends of course on the accuracy of the idealized rate- and state-variable law, which has to be tested case by case. For instance, wear and thermal effects, neglected here, may be very relevant in specific contexts. In view of that, we discuss an experimental setup that could be used to validate our findings. Our results mark a significant step forward in establishing a theoretical framework for control problems in the presence of friction and naturally pave the way for future experiments. |
| https://doi.org/10.1016/j.euromechsol.2024.105550 |
| arxiv |
Langevin dynamics with generalized time-reversal symmetry |
| D. Lucente, M. Baldovin, M. Viale, A. Vulpiani |
| When analyzing the equilibrium properties of a stochastic process, identifying the parity of the variables under time-reversal is imperative. This initial step is required to assess the presence of detailed balance, and to compute the entropy production rate, which is, otherwise, ambiguously defined. In this work we deal with stochastic processes whose underlying time-reversal symmetry cannot be reduced to the usual parity rules (namely, flip of the momentum sign). We provide a systematic method to build equilibrium Langevin dynamics starting from their reversible deterministic counterparts: this strategy can be applied, in particular, to all stable one-dimensional Hamiltonian dynamics, exploiting the time-reversal symmetry unveiled in the action-angle framework. The case of the Lotka-Volterra model is discussed as an example. We also show that other stochastic versions of this system violate time-reversal symmetry and are, therefore, intrinsically out of equilibrium. |
| https://doi.org/10.48550/arXiv.2504.05980 |
2024
| Physical Review E |
From noise on the sites to noise on the links: Discretizing the conserved Kardar-Parisi-Zhang equation in real space |
| A. Cavagna, J. Cristín, I. Giardina, M. Veca |
| Numerical analysis of conserved field dynamics has been generally performed with pseudospectral methods. Finite differences integration, the common procedure for nonconserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work we present a method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents α, β, and z in d=1 and in d=2. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of nonstandard lattices and on the random Euclidean graph. This is a unique numerical study of conserved field dynamics on an irregular topology, paving the way for a broad spectrum of possible applications. |
| https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064136 |
| Journal of Physics A: Mathematical and Theoretical |
Discrete Laplacian thermostat for flocks and swarms: the fully conserved Inertial Spin Model |
| A. Cavagna, J. Cristín, I. Giardina, T.S. Grigera, M. Veca |
| Experiments on bird flocks and midge swarms reveal that these natural systems are well described by an active theory in which conservation laws play a crucial role. By building a symplectic structure that couples the particles’ velocities to the generator of their internal rotations (spin), the Inertial Spin Model (ISM) reinstates a second-order temporal dynamics that captures many phenomenological traits of flocks and swarms. The reversible structure of the ISM predicts that the total spin is a constant of motion, the central conservation law responsible for all the novel dynamical features of the model. However, fluctuations and dissipation introduced in the original model to make it relax, violate the spin conservation law, so that the ISM aligns with the biophysical phenomenology only within finite-size regimes, beyond which the overdamped dynamics characteristic of the Vicsek model takes over. Here, we introduce a novel version of the ISM, in which the irreversible terms needed to relax the dynamics strictly respect the conservation of the spin. We perform a numerical investigation of the fully conservative model, exploring both the fixed-network case, which belongs to the equilibrium class of Model G, and the active case, characterized by self-propulsion of the agents and an out-of-equilibrium reshuffling of the underlying interaction network. Our simulations not only capture the correct spin wave phenomenology of the ordered phase, but they also yield dynamical critical exponents in the near-ordering phase that agree very well with the theoretical predictions. |
| https://iopscience.iop.org/article/10.1088/1751-8121/ad7ca0 |
| Physical Review E |
Inertial spin model of flocking with position-dependent forces |
| S. Carruitero, A. Costa Duran, G. Pisegna, M.B. Sturla, T.S. Grigera |
| We propose an extension to the inertial spin model (ISM) of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for onset of order provided by the Vicsek model. The inertial spin model (ISM) has only been formulated with an imitation (“ferromagnetic”) interaction between velocities. Here we show how to add position-dependent forces in the model, which allows to consider effects such as cohesion, excluded volume, confinement, and perturbation with external position-dependent field, and thus study this model without periodic boundary conditions. We study numerically a single particle with an harmonic confining field and compare it to a Brownian harmonic oscillator and to a harmonically confined active Browinian particle, finding qualitatively different behavior in the three cases. |
| https://doi.org/10.1103/PhysRevE.110.014408 |
| Physical Review A |
Self-diffusion in a strongly coupled non-neutral plasma |
| M. Baldovin, G. Vallet, G. Hagel, E. Trizac, C. Champenois |
| We propose a joint experimental and theoretical approach to measure the self-diffusion in a laser-cooled trapped ion cloud where part of the ions are shelved in a long-lived dark state. The role of the self-diffusion coefficient in the spatial organisation of the ions is deciphered, following from the good agreement between the experimental observations and the theoretical predictions. This comparison furthermore allows us to deduce the temperature of the sample. Protocols to measure the self-diffusion coefficient are discussed, in regard with the control that can be reached on the relevant timescales through the dressing of the atomic levels by laser fields. |
| https://doi.org/10.1103/PhysRevA.109.043116 |
| Journal of Statistical Physics |
Optimal control of underdamped systems: An analytic approach |
| J. Sanders, M. Baldovin, P. Muratore-Ginanneschi |
| Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale. |
| https://link.springer.com/article/10.1007/s10955-024-03320-w |
| arxiv |
Out of equilibrium response and fluctuation-dissipation violations across scales in flocking systems |
| F. Ferretti, I. Giardina, T.S. Grigera, G. Pisegna, M. Veca |
| Flocking systems are known to be strongly out of equilibrium. Energy input occurs at the individual level to ensure self-propulsion, and the individual motility in turn contributes to ordering, enhancing information propagation and strengthening collective motion. However, even beyond ordering, a crucial feature of natural aggregations is response. How, then, do off-equilibrium features affect the response of the system? In this work, we consider a minimal model of flocking and investigate response behavior under directional perturbations. We show that equilibrium dynamical fluctuation-dissipation relations between response and correlations are violated, both at the local and at the global level. The amount of violation peaks at the ordering transition, exactly as for the entropy production rate. Entropy is always produced locally and connected to the local fluctuation-dissipation violation via Harada-Sasa relationships. However, cooperative mechanisms close to the transition spread off-equilibrium effects to the whole system, producing an out of equilibrium response on the global scale. Our findings elucidate the role of activity and interactions in the cost repartition of collective behavior and explain what observed in experiments on natural living groups. |
| https://doi.org/10.48550/arXiv.2405.12874 |
| arxiv |
Optimal control of levitated nanoparticles through finite-stiffness confinement |
| M. Baldovin, I. Ben Yedder, C.A. Plata, D. Raynal, L. Rondin, E. Trizac, A. Prados |
| Optimal control of levitated particles subject to thermal fluctuations is a challenging problem, both from the theoretical and the experimental perspective. In this paper we compute the time-dependent harmonic confining potential that steers a Brownian particle between two assigned equilibrium states, in a prescribed time, with the minimum energetic cost. In our analysis we do not neglect inertial effects (thus addressing the general underdamped dynamics) and we assume, motivated by the experiments, that the stiffness of the confining potential cannot exceed prescribed bounds. We report the results of an experiment realizing the described protocol for an optically confined nanoparticle. The system is shown to reach the target state within accuracy, while spending less energy than other protocols that require the same time. The optimal protocol is also compared to an abrupt change of the confining stiffness, the latter involving an exponential relaxation to the target equilibrium state. Not only does our optimal protocol reach the target state in a finite time but it does so in a time significantly shorter than the characteristic timescale of the direct relaxation. The results presented in this paper are expected to have relevant applications in the design of optimal devices, e.g. engines at the nanoscale. |
| https://doi.org/10.48550/arXiv.2408.00043 |
| arxiv |
Thermalization is typical in large classical and quantum harmonic systems |
| M. Cattaneo, M. Baldovin, D. Lucente, P. Muratore-Ginanneschi, A. Vulpiani |
| We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in physically relevant random quadratic Hamiltonians, is typical for large systems (N >> 1) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from non-typical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and build a bridge between the classical and quantum theories of thermalization. |
| https://doi.org/10.48550/arXiv.2409.06489 |
| arxiv |
On the foundations of statistical mechanics |
| M. Baldovin, G. Gradenigo, A. Vulpiani, N. Zanghì |
| Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself, both for physicists and philosophers, and the obvious pedagogical motivations, there is a further, compelling reason for a thorough understanding of the subject. The fast development of models and methods at the edge of the established domain of the field requires indeed a deep reflection on the essential aspects of the theory, which are at the basis of its success. These elements should never be disregarded when trying to expand the domain of statistical mechanics to systems with novel, little known features. It is thus important to (re)consider in a careful way the main ingredients involved in the foundations of statistical mechanics. Among those, a primary role is covered by the dynamical aspects (e.g. presence of chaos), the emergence of collective features for large systems, and the use of probability in the building of a consistent statistical description of physical systems. With this goal in mind, in the present review we aim at providing a consistent picture of the state of the art of the subject, both in the classical and in the quantum realm. In particular, we will highlight the similarities of the key technical and conceptual steps with emphasis on the relevance of the many degrees of freedom, to justify the use of statistical ensembles in the two domains. |
| https://doi.org/10.48550/arXiv.2411.08709 |
2023
| Physical Review B |
Discrete Laplacian thermostat for spin systems with conserved dynamics |
| A. Cavagna, J. Cristín, I. Giardina, M. Veca |
| A well-established numerical technique to study the dynamics of spin systems in which symmetries and conservation laws play an important role is to microcanonically integrate their reversible equations of motion, obtaining thermalization through initial conditions drawn with the canonical distribution. In order to achieve a more realistic relaxation of the magnetic energy, numerically expensive methods that explicitly couple the spins to the underlying lattice are normally employed. Here we introduce a stochastic conservative thermostat that relaxes the magnetic energy while preserving the constant of motions, thus turning microcanonical spin dynamics into a conservative canonical dynamics, without actually simulating the lattice. We test the thermostat on the Heisenberg antiferromagnet in d=3 and show that the method reproduces the exact values of the static and dynamic critical exponents, while in the low-temperature phase it yields the correct spin wave phenomenology. Finally, we demonstrate that the relaxation coefficient of the new thermostat is quantitatively connected to the microscopic parameters of the spin-lattice coupling. |
| https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.224302 |
| Scientific Reports |
Characterization of lab-based swarms of Anopheles gambiae mosquitoes using 3D-video tracking |
| A. Cavagna, I. Giardina, M.A. Gucciardino, G. Iacomelli, M. Lombardi, S. Melillo, G. Monacchia, L. Parisi, M.J. Peirce, R. Spaccapelo |
| Mosquito copulation is a crucial determinant of its capacity to transmit malaria-causing Plasmodium parasites as well as underpinning several highly-anticipated vector control methodologies such as gene drive and sterile insect technique. For the anopheline mosquitoes responsible for African malaria transmission, mating takes place within crepuscular male swarms which females enter solely to mate. However, the mechanisms that regulate swarm structure or that govern mate choice remain opaque. We used 3D-video tracking approaches and computer vision algorithms developed for the study of other complex biological systems to document swarming behavior of a lab-adapted Anopheles gambiae line in a lab-based setting. By reconstructing trajectories of individual mosquitoes lasting up to 15.88 s, in swarms containing upwards of 200 participants, we documented swarm-like behavior in both males and females. In single sex swarms, encounters between individuals were fleeting (< 0.75 s). By contrast, in mixed swarms, we were able to detect 79 ‘brief encounters’ (> 0.75 s; < 2.5 s) and 17 longer-lived encounters (> 2.5 s). We also documented several examples of apparent male-male mating competition. These findings represent the first steps towards a more detailed and quantitative description of swarming and courtship behavior in one of the most important vectors of malaria. |
| https://www.nature.com/articles/s41598-023-34842-0 |
| Nature Physics |
Natural swarms in 3.99 dimensions |
| A. Cavagna, L. Di Carlo, I. Giardina, T.S. Grigera, S. Melillo, L. Parisi, G. Pisegna, M. Scandolo |
| The renormalization group is a key set of ideas and quantitative tools of statistical physics that allow for the calculation of universal quantities that encompass the behaviour of different kinds of collective systems. Extension of the predictive power of the renormalization group to collective biological systems would greatly strengthen the effort to put physical biology on a firm basis. Here we present a step in that direction by calculating the dynamical critical exponent z of natural swarms of insects using the renormalization group to order ϵ = 4 − d. We report the emergence of a novel fixed point, where both activity and inertia are relevant. In three dimensions, the critical exponent at the new fixed point is z = 1.35, in agreement with both experiments (1.37 ± 0.11) and numerical simulations (1.35 ± 0.04). Our results probe the power of the renormalization group for the quantitative description of collective behaviour, and suggest that universality may also play a decisive role in strongly correlated biological systems. |
| https://www.nature.com/articles/s41567-023-02028-0 |
| Ecological Indicators |
Testing for stationary dynamics in the Barro Colorado Island forest |
| A. Cavagna, H. Fort, T. S. Grigera |
| We analyse population dynamics in Barro Colorado Island (Panama) using census data of a 50 ha forest plot spanning 35 years, and address the question whether this community is in a stationary state. Individual species abundances show large fluctuations, but assessing stationariety requires discriminating random fluctuations from actual trends. This requires evaluating mean quantities as well as the structure (i.e. the correlations) of the fluctuations around this mean. We argue that a species average is the best surrogate for the theoretically required but unfeasible history average. We define the overlap, a species-averaged measure of composition similarity, which reveals that the BCI population dynamics is stationary but not static, displaying fluctuations with a characteristic time of around 15 years, two orders of magnitude less than previously estimated. |
| https://www.sciencedirect.com/science/article/pii/S1470160X23000225 |
| The European Physical Journal E |
Active Ising Models of flocking: a field-theoretic approach |
| M. Scandolo, J. Pausch, M.E. Cates |
| Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first-order transition from isotropic to flocked states whenever the self-propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking—an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self-propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state. |
| https://doi.org/10.1140/epje/s10189-023-00364-w |
| Physical Review Letters |
Revealing the nonequilibrium nature of a granular intruder: the crucial role of non-Gaussian behavior |
| D. Lucente, M. Viale, A. Gnoli, A. Puglisi, A. Vulpiani |
| The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a one-dimensional time series, such a goal becomes challenging. A paradigmatic example is the angular diffusion of a rotator immersed in a vibro-fluidized granular gas. Here, we experimentally observe that the rotator’s angular velocity exhibits significant differences with respect to an equilibrium process. Exploiting the presence of two relevant timescales and non-Gaussian velocity increments, we quantify the breakdown of time-reversal asymmetry, which would vanish in the case of a 1D Gaussian process. We deduce a new model for the massive probe, with two linearly coupled variables, incorporating both Gaussian and Poissonian noise, the latter motivated by the rarefied collisions with the granular bath particles. Our model reproduces the experiment in a range of densities, from dilute to moderately dense, with a meaningful dependence of the parameters on the density. We believe the framework proposed here opens the way to a more consistent and meaningful treatment of out-of-equilibrium and dissipative systems. |
| https://doi.org/10.1103/PhysRevLett.131.078201 |
| Journal of Statistical Mechanics: Theory and Experiment |
Statistical features of systems driven by non-Gaussian processes: theory and practice |
| D. Lucente, A. Puglisi, M. Viale, A. Vulpiani |
| Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here we consider a class of Markov processes described by Langevin equations driven by a mixture of Gaussian and Poissonian noises, focusing on their non-equilibrium properties. In particular, we prove that detailed balance does not hold even when correlation functions are symmetric under time reversal. In such cases, a breakdown of the time reversal symmetry can be highlighted by considering higher order correlation functions. Furthermore, the entropy production may be different from zero even for vanishing currents. We provide analytical expressions for the average entropy production rate in several cases. We also introduce a scale dependent estimate for entropy production, suitable for inference from experimental signals. The empirical entropy production allows us to discuss the role of spatial and temporal resolutions in characterizing non-equilibrium features. Finally, we revisit the Brownian gyrator introducing an additional Poissonian noise showing that it behaves as a two dimensional linear ratchet. It has also the property that when Onsager relations are satisfied its entropy production is positive although it is minimal. We conclude discussing estimates of entropy production for partially accessible systems, comparing our results with the lower bound provided by the thermodynamic uncertainty relations. |
| https://iopscience.iop.org/article/10.1088/1742-5468/ad063b |
2022
| Nature |
Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate |
| Q. Fontaine, D. Squizzato, F. Baboux, I. Amelio, A. Lemaître, M. Morassi, I. Sagnes, L. Le Gratiet, A. Harouri, M. Wouters, I. Carusotto, A. Amo, M. Richard, A. Minguzzi, L. Canet, S. Ravets, J. Bloch |
| Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces and of interfaces in bacterial colonies, and spin transport in quantum magnets all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space–time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar–Parisi–Zhang (KPZ) equation. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space–time scaling laws, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantum systems. |
| https://www.nature.com/articles/s41586-022-05001-8 |
| Physical Review E |
Renormalization group study of marginal ferromagnetism |
| A. Cavagna, A. Culla, T.S. Grigera |
| When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T = 0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension dc = 2, so in three dimensions the critical exponents acquire their free values, ν = 1/2 and η = 0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>dc. The numerical data fully confirm our theoretical results. |
| https://link.aps.org/doi/10.1103/PhysRevE.106.054136 |
| Nature Communications |
Marginal speed confinement resolves the conflict between correlation and control in collective behaviour |
| A. Cavagna, A. Culla, X. Feng, I. Giardina, T.S. Grigera, W. Kion-Crosby, S. Melillo, G. Pisegna, L. Postiglione, P. Villegas |
| Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group’s speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude. |
| https://www.nature.com/articles/s41467-022-29883-4 |
| Physical Review E |
Signatures of irreversibility in microscopic models of flocking |
| F. Ferretti, S. Grosse-Holz, C. Holmes, J. L. Shivers, I. Giardina, M. Thierry, A. M. Walczak |
| Flocking in d = 2 is a genuine nonequilibrium phenomenon for which irreversibility is an essential ingredient. We study a class of minimal flocking models whose only source of irreversibility is self-propulsion and use the entropy production rate (EPR) to quantify the departure from equilibrium across their phase diagrams. The EPR is maximal in the vicinity of the order-disorder transition, where reshuffling of the interaction network is fast. We show that signatures of irreversibility come in the form of asymmetries in the steady-state distribution of the flock’s microstates. These asymmetries occur as consequences of the time-reversal symmetry breaking in the considered self-propelled systems, independently of the interaction details. In the case of metric pairwise forces, they reduce to local asymmetries in the distribution of pairs of particles. This study suggests a possible use of pair asymmetries both to quantify the departure from equilibrium and to learn relevant information about aligning interaction potentials from data. |
| https://link.aps.org/doi/10.1103/PhysRevE.106.034608 |
| Physical Review E |
Renormalization group approach to connect discrete- and continuous-time descriptions of Gaussian processes |
| F. Ferretti, V. Chardès, T. Mora, A. M. Walczak, I. Giardina |
| Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme may perform very differently for the two tasks, if it is not accurate enough. Exact discretizations, which work equally well at any scale, are characterized by the property of invariance under coarse-graining. Motivated by this observation, we build an explicit renormalization group (RG) approach for Gaussian time series generated by autoregressive models. We show that the RG fixed points correspond to discretizations of linear SDEs, and only come in the form of first order Markov processes or non-Markovian ones. This fact provides an alternative explanation of why standard delay-vector embedding procedures fail in reconstructing partially observed noise-driven systems. We also suggest a possible effective Markovian discretization for the inference of partially observed underdamped equilibrium processes based on the exploitation of the Einstein relation. |
| https://link.aps.org/doi/10.1103/PhysRevE.105.044133 |
| Physical Review Research |
Inference of time irreversibility from incomplete information: Linear systems and its pitfalls |
| D. Lucente, A. Baldassarri, A. Puglisi, A. Vulpiani, M. Viale |
| Data from experiments and theoretical arguments are the two pillars sustaining the job of modeling physical systems through inference. In order to solve the inference problem, the data should satisfy certain conditions that depend also upon the particular questions addressed in a research. Here we focus on the characterization of systems in terms of a distance from equilibrium, typically the entropy production (time-reversal asymmetry) or the violation of the Kubo fluctuation-dissipation relation. We show how general, counterintuitive and negative for inference, is the problem of the impossibility to estimate the distance from equilibrium using a series of scalar data which have a Gaussian statistics. This impossibility occurs also when the data are correlated in time, and that is the most interesting case because it usually stems from a multi-dimensional linear Markovian system where there are many timescales associated to different variables and, possibly, thermal baths. Observing a single variable (or a linear combination of variables) results in a one-dimensional process which is always indistinguishable from an equilibrium one (unless a perturbation-response experiment is available). In a setting where only data analysis (and not new experiments) is allowed, we propose as a way out the combined use of different series of data acquired with different parameters. This strategy works when there is a sufficient knowledge of the connection between experimental parameters and model parameters. We also briefly discuss how such results emerge, similarly, in the context of Markov chains within certain coarse-graining schemes. Our conclusion is that the distance from equilibrium is related to quite a fine knowledge of the full phase space, and therefore typically hard to approximate in real experiments. |
| https://link.aps.org/doi/10.1103/PhysRevResearch.4.043103 |
| New Journal of Physics |
Evidence of fluctuation-induced first-order phase transition in active matter |
| D. Lucente, A. Baldassarri, A. Puglisi, A. Vulpiani, M. Viale |
| We investigate the effects of density fluctuations on the near-ordering phase of a flock by studying the Malthusian Toner–Tu theory. Because of the birth/death process, characteristic of this Malthusian model, density fluctuations are partially suppressed. We show that unlike its incompressible counterpart, where the absence of the density fluctuations renders the ordering phase transition similar to a second-order phase transition, in the Malthusian theory density fluctuations may turn the phase from continuous to first-order. We study the model using a perturbative renormalization group approach. At one loop, we find that the renormalization group flow drives the system in an unstable region, suggesting a fluctuation-induced first-order phase transition. |
| https://iopscience.iop.org/article/10.1088/1367-2630/aca9ed |
| Entropy |
Informational Entropy Threshold as a Physical Mechanism for Explaining Tree-Like Decision Making in Humans |
| J. Cristín, V. Méndez, D. Campos |
| While approaches based on physical grounds (such as the drift-diffusion model—DDM) have been exhaustively used in psychology and neuroscience to describe perceptual decision making in humans, similar approaches to complex situations, such as sequential (tree-like) decisions, are still scarce. For such scenarios that involve a reflective prospection of future options, we offer a plausible mechanism based on the idea that subjects can carry out an internal computation of the uncertainty about the different options available, which is computed through the corresponding Shannon entropy. When the amount of information gathered through sensory evidence is enough to reach a given threshold in the entropy, this will trigger the decision. Experimental evidence in favor of this entropy-based mechanism was provided by exploring human performance during navigation through a maze on a computer screen monitored with the help of eye trackers. In particular, our analysis allows us to prove that (i) prospection is effectively used by humans during such navigation tasks, and an indirect quantification of the level of prospection used is attainable; in addition, (ii) the distribution of decision times during the task exhibits power-law tails, a feature that our entropy-based mechanism is able to explain, unlike traditional (DDM-like) frameworks. |
| https://www.mdpi.com/1099-4300/24/12/1819 |
2021
| Journal of Statistical Physics |
Dynamical Renormalization Group for Mode-Coupling Field Theories with Solenoidal Constraint |
| A. Cavagna, L. Di Carlo, I. Giardina, T.S. Grigera, G. Pisegna, M. Scandolo |
| The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles’ velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields—density, velocity and spin—has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups. |
| https://link.springer.com/article/10.1007/s10955-021-02800-7 |
| Physical Review E |
Vicsek Model by Time-Interlaced Compression: a Dynamical Computable Information Density |
| A. Cavagna, P.M.Chaikin, D. Levine, S. Martiniani, A. Puglisi, M. Viale |
| Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of “phase” based on the standard concept of order parameter may therefore be complicated, and made even trickier by the lack of thermodynamic equilibrium. Compression-based entropies have been proved useful in recent years in describing the different phases of out-of-equilibrium systems. Here, we investigate the performance of a compression-based entropy, namely the Computable Information Density (CID), within the Vicsek model of collective motion. Our entropy is defined through a crude coarse-graining of the particle positions, in which the key role of velocities in the model only enters indirectly through the velocity-density coupling. We discover that such entropy is a valid tool in distinguishing the various noise regimes, including the crossover between an aligned and misaligned phase of the velocities, despite the fact that velocities are not used by this entropy. Furthermore, we unveil the subtle role of the time coordinate, unexplored in previous studies on the CID: a new encoding recipe, where space and time locality are both preserved on the same ground, is demonstrated to reduce the CID. Such an improvement is particularly significant when working with partial and/or corrupted data, as it is often the case in real biological experiments. |
| https://link.aps.org/doi/10.1103/PhysRevE.103.062141 |
| IEEE Transactions on Instrumentation and Measurement |
CoMo: A novel co-moving 3D camera system |
| A. Cavagna, X. Feng, S. Melillo, L. Parisi, L. Postiglione, P. Villegas |
| Motivated by the theoretical interest in reconstructing long 3D trajectories of individual birds in large flocks, we developed CoMo, a co-moving camera system of two synchronized high speed cameras coupled with rotational stages, which allow us to dynamically follow the motion of a target flock. With the rotation of the cameras we overcome the limitations of standard static systems that restrict the duration of the collected data to the short interval of time in which targets are in the cameras common field of view, but at the same time we change in time the external parameters of the system, which have then to be calibrated frame-by-frame. We address the calibration of the external parameters measuring the position of the cameras and their three angles of yaw, pitch and roll in the system home configuration (rotational stage at an angle equal to 0 ◦) and combining this static information with the time dependent rotation due to the stages. We evaluate the robustness and accuracy of the system by comparing reconstructed and measured 3D distances in what we call 3D tests, which show a relative error of the order of 1%. The novelty of the work presented in this paper is not only on the system itself, but also on the approach we use in the tests, which we show to be a very powerful tool in detecting and fixing calibration inaccuracies and that, for this reason, may be relevant for a broad audience. |
| https://ieeexplore.ieee.org/document/9409130 |
| Physical Review Research |
Equilibrium to off-equilibrium crossover in homogeneous active matter |
| A. Cavagna, L. Di Carlo, I. Giardina, T.S. Grigera, G. Pisegna |
| We study the crossover between equilibrium and off-equilibrium dynamical universality classes in the Vicsek model near its ordering transition. Starting from the incompressible hydrodynamic theory of Chen et al. [Critical phenomenon of the order-disorder transition in incompressible active fluids, New J. Phys. 17, 042002 (2015)], we show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent z = 2, and the off-equilibrium active fixed point, with z = 1.7 (in d = 3). We run simulations of the classic Vicsek model in the near-ordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in remarkable agreement with the RG prediction. The equilibrium to off-equilibrium crossover is ruled by a characteristic length scale, beyond which active dynamics takes over. The larger the activity is, the smaller is such a length scale, suggesting the existence of a general trade-off between activity and the system’s size in determining the dynamical universality class of active matter. |
| https://link.aps.org/doi/10.1103/PhysRevResearch.3.013210 |
| Royal Society |
Joint assessment of density correlations and fluctuations for analysing spatial tree patterns |
| P. Villegas, A. Cavagna, M. Cencini, H. Fort, T.S. Grigera |
| Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of tropical rainforests, as demonstrated, e.g. in the 50 ha tropical forest plot on Barro Colorado Island, Panama. These kinds of plots have been crucial to shed light on diverse qualitative features, emerging both at the single-species or the community level, like the spatial aggregation or clustering at short scales. Here, we build on the progress made in the study of the density correlation functions applied to biological systems, focusing on the importance of accurately defining the borders of the set of trees, and removing the induced biases. We also pinpoint the importance of combining the study of correlations with the scale dependence of fluctuations in density, which are linked to the well-known empirical Taylor’s power law. Density correlations and fluctuations, in conjunction, provide a unique opportunity to interpret the behaviours and, possibly, to allow comparisons between data and models. We also study such quantities in models of spatial patterns and, in particular, we find that a spatially explicit neutral model generates patterns with many qualitative features in common with the empirical ones. |
| https://royalsocietypublishing.org/doi/10.1098/rsos.202200 |
2020
| Physical Review X |
Building general Langevin models from discrete data sets |
| F. Ferretti, V. Chardès, T. Mora, A. M. Walczak, I. Giardina |
| Experiments revealed inertial signatures in the effective dynamics of natural flocks of starlings and swarms of midges at their observational space-time scales. A quantitative assessment of the damping regime in which these systems operate may bring relevant information for the understanding of their dynamic properties and function. Learning from empirical observations is a long-standing goal in physics, but even today it can be often harder than expected. Building a stochastic model with memory from discrete time series is a challenging task, due to the non-Markovian character of the observed process. In the search for a robust inference method for our birds’ data, we developed a novel maximum likelihood scheme for non-Markovian dynamics with linear dissipation. Its potential application is not restricted to simple underdamped equilibrium models, but it can be implemented also in out-of-equilibrium and large size systems. |
| https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031018 |
2019
| Physical Review Letters |
Dynamical Renormalization Group approach to the collective behavior of swarms |
| A.Cavagna, L. Di Carlo, I. Giardina, L. Grandinetti, T. S. Grigera, G. Pisegna |
| The dynamical scaling hypothesis states that, for systems at the critical point the correlation length is linked to the characteristic relaxation time through the dynamic critical exponent z. Experimental results show that swarms of insects satisfy this property exhibiting an exponent z ≈1.2. Searching for a model able to reproduce this result, we study the critical properties of model with non-dissipative couplings. Using the Dynamical Renormalization Group technique, and working in the fixed network approximation, we find a crossover from a non-dissipative fixed point (z=d/2) to a dissipative ( z=2) fixed point. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system. The value z=d/2 in 3d is significantly closer to the experimental value, then the value found numerically in fully dissipative models z =1.7. This result suggests that mode coupling interaction is a key ingredient to build a theory of natural swarms close to the experiments. Further investigations including the self-propelled nature of the particles are necessary to embed the out-of-equilibrium essence of these biological systems. |
| https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.123.268001″ |
| https://journals.aps.org/pre/pdf/10.1103/PhysRevE.100.062130 |
| Physical Review E |
Renormalization group crossover in the critical dynamics of field theories with mode coupling terms |
| A. Cavagna, L. Di Carlo, I. Giardina, L. Grandinetti, T.S. Grigera, G. Pisegna |
| Motivated by the collective behavior of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. Under a fixed-network approximation, we perform a dynamical renormalization group calculation at one loop in the near-critical disordered region, and we show that the violation of momentum conservation generates a crossover between an unstable fixed point, characterized by a dynamic critical exponent z=d/2, and a stable fixed point with z=2. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent κ = 4/d. The crossover is regulated by a conservation length scale R0, given by the ratio between the transport coefficient and the effective friction, which is larger as the dissipation is smaller: Beyond R0, the stable fixed point dominates, while at shorter distances dynamics is ruled by the unstable fixed point and critical exponent, a behavior which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents z = 3/2 and z = 2 in the critical slowdown of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step toward reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases. |
| https://link.aps.org/doi/10.1103/PhysRevE.100.062130 |
| Comptes Rendus Physique |
Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks |
| A.Cavagna, A. Culla, L. Di Carlo, I. Giardina, T.S. Grigera |
| We introduced and studied a novel ferromagnetic model, suitable to reproduce a fascinating statistical property of starlings speeds in their flocking phase. From experimental data one finds that, in a strongly polarized flock, speed’s fluctuations are correlated on a characteristic length that is proportional to the system’s size, i.e. speed correlations are scale-free. We show that, using our “marginal” model, it is possible to reproduce this specific and unusual phenomenology, even in the equilibrium case. The key idea is to consider a bounding potential for the single-particle speed that has zero curvature. A novel zero-temperature critical point emerges and the model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in analogy with experimental data of natural flocks. Our tasks now are many: first of all, we will investigate more deeply the nature of the “marginal” scale-free behaviour of the model, extracting, in a numerical and a rigorous way, the critical exponents. Then, we will closely compare the statistical field theory, built from our microscopic model, to the experimental data. |
| https://www.sciencedirect.com/science/article/pii/S1631070519300374 |