On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems

Sarracino, Alessandro; Vulpiani, Angelo

doi:10.1063/1.5110262

Cited by 40 publications

(34 citation statements)

References 132 publications

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“…As is clear from scanning the vast literature on the subject, there are many different versions of response theory. Apart from standard treatments in text books such as [12][13][14][15][16], they include the papers [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] to which we refer for other approaches and results. The originality of our approach is to start from dynamical ensembles on path-space.…”

Section: General Question and Ambitionsmentioning

confidence: 99%

Response Theory: A Trajectory-Based Approach

Maes

2020

Front. Phys.

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We collect recent results on deriving useful response relations also for non-equilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation-dissipation relations in equilibrium. For non-equilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a non-equilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in non-equilibrium statistical mechanics.

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Section: General Question and Ambitionsmentioning

confidence: 99%

Response Theory: A Trajectory-Based Approach

Maes

2020

Front. Phys.

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“…This force replaces the microscopic details of the system that, in general, are related to complicate internal mechanisms of energy transduction and involve an intrinsic source of strong deviation from thermodynamic equilibrium. Except for special cases, the steadystate properties of these non-equilibrium models are not known analytically or without approximations, and thus FDR of class A remain in implicit forms [23,24]. Explicit expressions can be worked out in the limit of small persistence time τ, with the first example obtained in [25].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation–Dissipation Relations in Active Matter Systems

2021

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We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.

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“…The relation between ongoing and stimulated activity can be addressed theoretically within the general framework of statistical physics, by means of the fluctuation-dissipation relations, connecting the spontaneous fluctuations of a system with the response function to external perturbations. Recently, these relations have been extended beyond the context of standard thermodynamics, to nonequilibrium systems, such as active and biological matter [14][15][16][17][18][19]. These relations hold for a wide variety of physical systems, not necessarily at the critical point.…”

Section: Introductionmentioning

confidence: 99%

Predicting brain evoked response to external stimuli from temporal correlations of spontaneous activity

Sarracino

Arviv

Shriki

et al. 2020

Phys. Rev. Research

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The relation between spontaneous and stimulated global brain activity is a fundamental problem in the understanding of brain functions. This question is investigated both theoretically and experimentally within the context of nonequilibrium fluctuation-dissipation relations. We consider the stochastic coarse-grained Wilson-Cowan model in the linear noise approximation and compare analytical results to experimental data from magnetoencephalography of the human brain. The short-time behavior of the autocorrelation function for spontaneous activity is characterized by a double-exponential decay, with two characteristic times, differing by two orders of magnitude. Conversely, the response function exhibits a single-exponential decay in agreement with experimental data for evoked activity under visual stimulation. Results suggest that the brain response to weak external stimuli can be predicted from the observation of spontaneous activity and pave the way to controlled experiments on the brain response under different external perturbations.

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On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems

Cited by 40 publications

References 132 publications

Response Theory: A Trajectory-Based Approach

Response Theory: A Trajectory-Based Approach

Fluctuation–Dissipation Relations in Active Matter Systems

Predicting brain evoked response to external stimuli from temporal correlations of spontaneous activity

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