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Fluctuation relations for diffusion process
 Commun. Math. Phys
"... 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 timerever ..."
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Cited by 21 (6 self)
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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 timereversed 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. 1
Wijland: Thermodynamic formalism for systems with Markov dynamics
 J. Stat. Phys
, 2008
"... The thermodynamic formalism allows one to access the chaotic properties of equilibrium and outofequilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not sui ..."
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Cited by 20 (3 self)
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The thermodynamic formalism allows one to access the chaotic properties of equilibrium and outofequilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism –a dynamical Gibbs ensemble construction– to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the muchstudied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window. 1 1
A.: Relevance of initial and final conditions for the Fluctuation Relation in Markov processes
, 2006
"... Abstract. Numerical observations on a Markov chain and on the continuous Markov process performed by a granular tracer show that the “usual ” fluctuation relation for a given observable is not verified for finite (but arbitrarily large) times. This suggests that some terms which are usually expected ..."
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Cited by 12 (6 self)
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Abstract. Numerical observations on a Markov chain and on the continuous Markov process performed by a granular tracer show that the “usual ” fluctuation relation for a given observable is not verified for finite (but arbitrarily large) times. This suggests that some terms which are usually expected to be negligible, i.e. “border terms ” dependent only on initial and final states, in fact cannot be neglected. Furthermore, the Markov chain and the granular tracer behave in a quite similar fashion. Initial and final conditions for the fluctuation Relation in Markov processes 2 1.
On causally asymmetric versions of Occam’s Razor and their relation to thermodynamics
, 2007
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FLUCTUATIONS RELATIONS for SEMICLASSICAL SINGLEMODE LASER
, 810
"... Over last decades, the study of laser fluctuations has shown that laser theory may be regarded as a prototypical example of a nonlinear nonequilibrium problem. The present paper discusses the fluctuation relations, recently derived in nonequilibrium statistical mechanics, in the context of the semic ..."
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Cited by 1 (0 self)
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Over last decades, the study of laser fluctuations has shown that laser theory may be regarded as a prototypical example of a nonlinear nonequilibrium problem. The present paper discusses the fluctuation relations, recently derived in nonequilibrium statistical mechanics, in the context of the semiclassical laser theory. 1
Large deviations and Gallavotti–Cohen principle for dissipative PDE’s with rough noise
, 2014
"... We study a class of dissipative PDE’s perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a nondegenerate law, we prove t ..."
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We study a class of dissipative PDE’s perturbed by an unbounded kick force. Under some natural assumptions, the restrictions of solutions to integer times form a homogeneous Markov process. Assuming that the noise is rough with respect to the space variables and has a nondegenerate law, we prove that the system in question satisfies a large deviation principle (LDP) in τtopology. Under some additional hypotheses, we establish a Gallavotti–Cohen type symmetry for the rate function of an entropy production functional and the strict positivity and finiteness of the mean entropy production in the stationary regime. The latter result is applicable to PDE’s with strong nonlinear dissipation.
Numéro d'ordre: 489 Numéro attribué par la bibliothèque: 07ENSL0489 THÈSE
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Physics Reports 461 (2008) 111195 Contents lists available at ScienceDirect Physics Reports
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0Visibility Algorithms: A Short Review
"... Disregarding any underlying process (and therefore any physical, chemical, economical or whichever meaning of its mere numeric values), we can consider a time series just as an ordered set of values and play the naive mathematical game of turning this set into a different ..."
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Disregarding any underlying process (and therefore any physical, chemical, economical or whichever meaning of its mere numeric values), we can consider a time series just as an ordered set of values and play the naive mathematical game of turning this set into a different
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"... Work and heat probability distributions in outofequilibrium systems ..."
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