arXiv subjects

Massimiliano Viale

Publications and source records attributed to Massimiliano Viale.

At least 19 recordsLinked to original sources

arXiv2026

Thermal equilibrium with generalized time-reversal symmetry

In the study of stochastic processes, identifying the parity under time-reversal is essential to verify detailed balance, and to compute the entropy production rate (which is, otherwise, ambiguously defined). While in many cases the correct time-reversal symmetry is suggested by physical arguments, for generic processes the identification is not trivial: as a result, systems at thermal equilibrium may be mistakenly interpreted as non-equilibrium ones. We focus on the reversible deterministic dynamics of a slow variable coupled to many degrees of freedom acting as a thermal bath. We show that the time-reversal symmetry of the slow variable is preserved when passing to an effective stochastic description, independently of the nature of the bath. In turn, for generic 2-dimensional continuous Markov processes, we provide a criterion to identify the time-reversal parity rules under which the dynamics is at equilibrium (if any). The case of the Lotka-Volterra model is discussed as an example.

cond-mat.stat-mech↗

arXiv2024

Conceptual and practical approaches for investigating irreversible processes

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 [1]), 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.

cond-mat.stat-mech↗

arXiv2024

Response of Worm-like Chains to Traveling-Wave Active Forces

We present a simplified theory for semiflexible flagella under the action of a traveling-wave perturbation that emulates the organized active forces generated by molecular motors, capable of inducing beating patterns to the filament. By modeling the flagellum as a worm-like chain (WLC), we explore the interplay (competition) between the externally applied perturbation and the intrinsic bending rigidity of the filament. Our analysis aims to understand how this interplay can lead to a selection of conformations with the spatiotemporal behavior resembling the beating dynamics of axonemes such as those in sperm tails, in Chlamydomonas cilia, or eukaryotic flagella in general. Through a systematic analysis of the WLC's response to traveling-wave perturbations, we try to identify the key parameters that mostly influence the flagellar motion and shape its beating-like profiles.

cond-mat.soft↗

arXiv2023

Statistical features of systems driven by non-Gaussian processes: theory & practice

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.

cond-mat.stat-mech↗

arXiv2023

Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior

The characterization of the distance from equilibrium is a debated problem in particular in the treatment of experimental signals. If the signal is a 1-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 significative differences with respect to an equilibrium process. Exploiting the presence of two relevant time-scales 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.

cond-mat.stat-mech↗

arXiv2022

Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls

Data from experiments and theoretical arguments are the two pillars sustaining the job of modelling 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, counter-intuitive 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 time-scales 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.

cond-mat.stat-mech↗

arXiv2020

Vicsek Model by Time-Interlaced Compression: a Dynamical Computable Information Density

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.

cond-mat.stat-mech↗

arXiv2019

Comment on "Velocity and Speed Correlations in Hamiltonian Flocks" by M. Casiulis et al. [arXiv:1911.06042]

In arXiv:1911.06042v1 M. Casiulis et al. study a Hamiltonian model in which rigid rotations of moving clusters give rise to scale-free correlations of velocity and speed. M. Casiulis et al. compare correlations in their model to those observed in real flocks of birds and claim that rigid-body rotations provide an explanation that stands in contrast with, and it is simpler than, previously proposed explanations of correlations in bird flocks, namely Goldstone modes in the velocity orientations and marginal (or near-critical) modes in the speed. Here, we show that the rigid rotation scenario is completely inconsistent with a large body of well-established experimental evidence on real flocks of birds, and it therefore does not provide an appropriate explanation for the observed phenomenology.

physics.bio-ph↗

arXiv2016

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws

Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect the propagation across the system of a signal triggered by some perturbation. However, for field experiments this method is inefficient, as the possibilities of the observer to perturb the group are limited and empirical observations must rely on rare natural perturbations. An alternative way is to use spatio-temporal correlations to assess the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. We test the approach on ground truth data provided by numerical simulations in three dimensions of two models of collective behaviour characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an un- derdamped inertial dynamics. By using dynamical finite size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.

cond-mat.stat-mech↗

arXiv2016

Local equilibrium in bird flocks

The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. The effect of this off-equilibrium element is well studied theoretically, but its impact on actual biological groups deserves more experimental attention. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accodomates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment happens on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.

q-bio.PE↗

arXiv2016

Non-symmetric interactions trigger collective swings in globally ordered systems

Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing with system size. Several biological systems, however, are less stable than their physical analogues and spontaneously change their global state on relatively short timescales. In this paper we show that there are two crucial ingredients in these systems that enhance the effect of noise, leading to collective changes of state: the non-symmetric nature of interactions between individuals, and the presence of local heterogeneities in the topology of the network. The consequences of these features can be larger the larger the system size leading to a localization of the fluctuation modes and a relaxation time that remains finite in the thermodynamic limit. The system keeps changing its global state in time, being constantly driven out of equilibrium by spontaneous fluctuations. Our results explain what is observed in several living and social systems and are consistent with recent experimental data on bird flocks and other animal groups.

cond-mat.stat-mech↗

arXiv2015

Towards a tracking algorithm based on the clustering of spatio-temporal clouds of points

The interest in 3D dynamical tracking is growing in fields such as robotics, biology and fluid dynamics. Recently, a major source of progress in 3D tracking has been the study of collective behaviour in biological systems, where the trajectories of individual animals moving within large and dense groups need to be reconstructed to understand the behavioural interaction rules. Experimental data in this field are generally noisy and at low spatial resolution, so that individuals appear as small featureless objects and trajectories must be retrieved by making use of epipolar information only. Moreover, optical occlusions often occur: in a multi-camera system one or more objects become indistinguishable in one view, potentially jeopardizing the conservation of identity over long-time trajectories. The most advanced 3D tracking algorithms overcome optical occlusions making use of set-cover techniques, which however have to solve NP-hard optimization problems. Moreover, current methods are not able to cope with occlusions arising from actual physical proximity of objects in 3D space. Here, we present a new method designed to work directly in 3D space and time, creating (3D+1) clouds of points representing the full spatio-temporal evolution of the moving targets. We can then use a simple connected components labeling routine, which is linear in time, to solve optical occlusions, hence lowering from NP to P the complexity of the problem. Finally, we use normalized cut spectral clustering to tackle 3D physical proximity.

cs.CV↗

arXiv2015

Error control in the set-up of stereo camera systems for 3d animal tracking

Three-dimensional tracking of animal systems is the key to the comprehension of collective behavior. Experimental data collected via a stereo camera system allow the reconstruction of the 3d trajectories of each individual in the group. Trajectories can then be used to compute some quantities of interest to better understand collective motion, such as velocities, distances between individuals and correlation functions. The reliability of the retrieved trajectories is strictly related to the accuracy of the 3d reconstruction. In this paper, we perform a careful analysis of the most significant errors affecting 3d reconstruction, showing how the accuracy depends on the camera system set-up and on the precision of the calibration parameters.

q-bio.QM↗

arXiv2015

GReTA - a novel Global and Recursive Tracking Algorithm in three dimensions

Tracking multiple moving targets allows quantitative measure of the dynamic behavior in systems as diverse as animal groups in biology, turbulence in fluid dynamics and crowd and traffic control. In three dimensions, tracking several targets becomes increasingly hard since optical occlusions are very likely, i.e. two featureless targets frequently overlap for several frames. Occlusions are particularly frequent in biological groups such as bird flocks, fish schools, and insect swarms, a fact that has severely limited collective animal behavior field studies in the past. This paper presents a 3D tracking method that is robust in the case of severe occlusions. To ensure robustness, we adopt a global optimization approach that works on all objects and frames at once. To achieve practicality and scalability, we employ a divide and conquer formulation, thanks to which the computational complexity of the problem is reduced by orders of magnitude. We tested our algorithm with synthetic data, with experimental data of bird flocks and insect swarms and with public benchmark datasets, and show that our system yields high quality trajectories for hundreds of moving targets with severe overlap. The results obtained on very heterogeneous data show the potential applicability of our method to the most diverse experimental situations.

q-bio.QM↗

arXiv2015

Short-range interaction vs long-range correlation in bird flocks

Bird flocks are a paradigmatic example of collective motion. One of the prominent experimental traits discovered about flocks is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the Maximum Entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between birds. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.

physics.bio-ph↗

arXiv2015

Flocking and turning: a new model for self-organized collective motion

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.

cond-mat.stat-mech↗

arXiv2014

Emergence of collective changes in travel direction of starling flocks from individual birds fluctuations

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external perturbation, such as the presence of a predator, recent studies show that such directional switching can also emerge from the intrinsic fluctuations in the individual behaviour. However, the cause and the mechanism by which such collective changes of direction occur are not fully understood yet. Here, we present an experimental study of spontaneous collective turns in natural flocks of starlings. We employ a recently developed tracking algorithm to reconstruct three-dimensional trajectories of each individual bird in the flock for the whole duration of a turning event. Our approach enables us to analyze changes in the individual behavior of every group member and reveal the emergent dynamics of turning. We show that spontaneous turns start from individuals located at the elongated edges of the flocks, and then propagate through the group. We find that birds on the edges deviate from the mean direction of motion much more frequently than other individuals, indicating that persistent localized fluctuations are the crucial ingredient for triggering a collective directional change. Finally, we quantitatively show that birds follow equal radius paths during turning allowing the flock to change orientation and redistribute risky locations among group members. The whole process of turning is a remarkable example of how a self-organized system can sustain collective changes and reorganize, while retaining coherence.

physics.bio-ph↗

arXiv2014

Silent Flocks

Experiments find coherent information transfer through biological groups on length and time scales distinctly below those on which asymptotically correct hydrodynamic theories apply. We present here a new continuum theory of collective motion coupling the velocity and density fields of Toner and Tu to the inertial spin field recently introduced to describe information propagation in natural flocks of birds. The long-wavelength limit of the new equations reproduces Toner-Tu theory, while at shorter wavelengths (or, equivalently, smaller damping), spin fluctuations dominate over density fluctuations and second sound propagation of the kind observed in real flocks emerges. We study the dispersion relation of the new theory and find that when the speed of second sound is large, a gap sharply separates first from second sound modes. This gap implies the existence of `silent' flocks, namely medium-sized systems across which neither first nor second sound can propagate.

cond-mat.stat-mech↗