On the range of validity of the fluctuation theorem for stochastic Markovian dynamics

Rákos, A.; Harris, Rosemary J.

doi:10.1088/1742-5468/2008/05/p05005

Cited by 62 publications

(107 citation statements)

References 45 publications

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“…Along similar lines, Rákos and Harris have recently shown [30] that infinite state spaces can result in the divergence of the boundary terms, causing a breakdown of the Gallavotti-Cohen symmetry. 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).…”

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confidence: 80%

“…We consider in particular a Markov chain on a finite state space, whose infinitesimal generator is a continuous and periodic function of time but only required to be irreducible at a single moment. The finiteness of the state space ensures that the complexity of the model is isolated within the time dimension, avoiding in particular the issues raised in [30]. Such a process can be used to model phenomena as diverse as the fluctuation-driven transport of molecular motors [1], stochastic resonance in lasers and neuron firing [13], quasienergy banding in periodically-driven mesoscopic electric circuits [3], and seasonality in population dynamics [31], as well as periodically-driven deterministic processes amenable to coarse-graining.…”

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confidence: 99%

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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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confidence: 80%

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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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“…The first limit shown in (235) states that the most probable escape time scales as τ e V * / as → 0. From this concentration result, the second limit follows.…”

Section: Large Deviations For Derived Quantitiesmentioning

confidence: 99%

The large deviation approach to statistical mechanics

2009

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The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.PACS numbers: 65.40.Gr, Typeset by REVT E X arXiv:0804.0327v2 [cond-mat.stat-mech]

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“…This gives rise to exponential tails in the pdf of Q and is signaled by the presence of singularities in the corresponding characteristic function. Such temporal "boundary" effects that take place in systems with unbounded potentials are now well-documented, both theoretically [6][7][8][9][10][11][12][13][14][15][16][17] and experimentally [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Heat fluctuations for underdamped Langevin dynamics

Rosinberg¹,

Tarjus²,

Munakata³

2016

EPL

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Fluctuation theorems play a central role in nonequilibrium physics and stochastic thermodynamics. Here we derive an integral fluctuation theorem for the dissipated heat in systems governed by an underdamped Langevin dynamics. We show that this identity may be used to predict the occurrence of extreme events leading to exponential tails in the probability distribution functions of the heat and related quantities.

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On the range of validity of the fluctuation theorem for stochastic Markovian dynamics

Cited by 62 publications

References 45 publications

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

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

The large deviation approach to statistical mechanics

Heat fluctuations for underdamped Langevin dynamics

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