Chaotic Hypothesis, Fluctuation Theorem and Singularities

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.

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“…On the contrary, unbounded ϕT may give contributions to the large deviations statistics [82,9,85,69]. For the deterministic dynamics where…”

Section: Transient Versus Stationary Fluctuation Relationsmentioning

confidence: 99%

Fluctuation Relations for Diffusion Processes

Chétrite

Gawędzki

2008

Commun. Math. Phys.

150

349

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“…It is unclear, however, whether this breakdown, which arises from the failure of the Hamiltonian operator to satisfy Kurchan's nondegeneracy requirement, is really a function of the state space's cardinality as much as its non-compactness (the state space of a Markov chain being effectively endowed with the discrete metric). In the case of deterministic dynamics, Bonetto et al have argued that apparent violations of AFTs by particle systems with singularities in the interparticle potential (owing, for example, to hard cores) can be corrected by subtracting "unphysical" singular terms from the phase space contraction rate [2].…”

mentioning

confidence: 99%

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Shargel¹,

Chou

2009

J Stat Phys

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Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes of continuous-time deterministic and stochastic processes, but always under the assumption that the forces driving the system are time independent, and often relying on the existence of a limiting ergodic distribution. In this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous-time processes without a stationary distribution, considering specifically a finite state Markov chain driven by periodic transition rates. We find that for both entropy production and heat dissipation, the usual Gallavotti-Cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process, in which the trajectory and the driving protocol have been time-reversed. The effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process, and vice-versa, revealing that the distributions of fluctuations in universes in which time moves forward and backward are related. As an additional result, the asymptotic time-averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics.

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“…Fluctuations and large deviations functions, however, may keep the memory of those terms [37][38][39].…”

Section: Equilibrium Bath With a Non-conservative Force: Standard Entmentioning

confidence: 99%

Clausius Relation for Active Particles: What Can We Learn from Fluctuations

Puglisi

Marconi

2017

Entropy

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Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom-or arbitrariness-appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.

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Chaotic Hypothesis, Fluctuation Theorem and Singularities

Cited by 87 publications

References 38 publications

Fluctuation Relations for Diffusion Processes

Fluctuation Relations for Diffusion Processes

Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains

Clausius Relation for Active Particles: What Can We Learn from Fluctuations

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