Large Deviations and a Fluctuation Symmetry for Chaotic Homeomorphisms
Christian Maes,Evgeny Verbitskiy +1 more
TLDR
In this article, the authors considered expansive homeomorphisms with the specification property and gave a new simple proof of a large deviation principle for Gibbs measures corresponding to a regular potential and established a general symmetry of the rate function for the large deviations of the antisymmetric part, under time-reversal, of the potential.Abstract:
We consider expansive homeomorphisms with the specification property We give a new simple proof of a large deviation principle for Gibbs measures corresponding to a regular potential and we establish a general symmetry of the rate function for the large deviations of the antisymmetric part, under time-reversal, of the potential This generalizes the Gallavotti-Cohen fluctuation theorem to a larger class of chaotic systemsread more
Citations
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Journal ArticleDOI
The large deviation approach to statistical mechanics
TL;DR: The theory of large deviations as mentioned in this paper is concerned with the exponential decay of probabilities of large fluctuations in random systems, and it provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations.
Journal ArticleDOI
The large deviation approach to statistical mechanics
TL;DR: The theory of large deviations as discussed by the authors is concerned with the exponential decay of probabilities of large fluctuations in random systems, and it provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations.
Book ChapterDOI
On the origin and the use of fluctuation relations for the entropy
TL;DR: In this paper, a unifying framework for entropy symmetries under time-reversal has been proposed, and an algorithm to derive them is presented, which can be seen as a generalization of fluctuation-dissipation relations.
Journal ArticleDOI
Frenesy: Time-symmetric dynamical activity in nonequilibria
TL;DR: The concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime is reviewed in this article, where the breaking of time-reversal invariance is quantified via the entropy flux, and the consequences for fluctuation and response theory.
Journal ArticleDOI
Fluctuation relation for a Lévy particle.
Hugo Touchette,E. G. D. Cohen +1 more
TL;DR: In the stationary regime, the probability density of the work is found to have "fat" power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian, leading to a strong violation of existing fluctuation theorems.
References
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Introduction to the modern theory of dynamical systems
Anatole Katok,Boris Hasselblatt +1 more
TL;DR: In this article, Katok and Mendoza introduced the concept of asymptotic invariants for low-dimensional dynamical systems and their application in local hyperbolic theory.
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TL;DR: The first part of the text as discussed by the authors provides an introduction to ergodic theory suitable for readers knowing basic measure theory, including recurrence properties, mixing properties, the Birkhoff Ergodic theorem, isomorphism, and entropy theory.
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Entropy, large deviations, and statistical mechanics
TL;DR: In this paper, the authors introduce the concept of large deviations for random variables with a finite state space, which is a generalization of the notion of large deviation for random vectors.
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Probability of second law violations in shearing steady states.
TL;DR: An expression for the probability of fluctuations in the shear stress of a fluid in a nonequilibrium steady state far from equilibrium is given and a formula for the ratio that, for a finite time, theShear stress reverse sign is violating the second law of thermodynamics.
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Dynamical ensembles in stationary states
TL;DR: In this paper, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general is proposed, which leads to the identification of a unique distribution μ describing the asymptotic properties of the system for initial data randomly chosen with respect to a uniform distribution on phase space.
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