Mathematical Theory of Nonequilibrium Steady States

Jiang, Da-Quan; Qian, Min; Qian, Minping

doi:10.1007/b94615

Cited by 239 publications

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“…By the Gärtner-Ellis theorem and equalities analogous to (19), this implies the fluctuation theorem symmetry.…”

Section: Remark 42 Equationmentioning

confidence: 85%

“…which reduces to the usual Gallavotti-Cohen symmetry when the generator is a symmetric function of time within each driving period, in which case the backward path measure reduces to the path-reversed measure P [0,t] • r considered in [18,19,24,26,27]. (Note that even in this scenario these authors' results do not apply, because the dynamics remain time-dependent and non-stationary.)…”

Section: Definitions and Setupmentioning

confidence: 99%

“…5. For a comprehensive justification of the definitions used above for entropy production and heat dissipation, see [17,19,26,27,33]. …”

Section: Definitions and Setupmentioning

confidence: 99%

“…Kurchan first proved an AFT [21] for the entropy production of Langevin processes under the assumption of nondegeneracy for the maximum eigenvalue of their evolution operator, and Lebowitz and Spohn then proved it [24] for the heat dissipation of time-homogeneous Markov chains and Itô diffusions, whose assumed limiting stationary distribution guarantees this condition. The cases of continuous and discrete time Markov chains were handled in a rigorous fashion by Jiang et al [18,19], and Ge et al extended the discrete time case to include time-periodic inhomogeneities in the transition matrix [16]. Maes took a different approach from the others, studying the dynamics of finite volume Gibbs states on Z d under general space-time potentials [25].…”

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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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“…By the Gärtner-Ellis theorem and equalities analogous to (19), this implies the fluctuation theorem symmetry.…”

Section: Remark 42 Equationmentioning

confidence: 85%

Section: Definitions and Setupmentioning

confidence: 99%

“…5. For a comprehensive justification of the definitions used above for entropy production and heat dissipation, see [17,19,26,27,33]. …”

Section: Definitions and Setupmentioning

confidence: 99%

mentioning

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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“…Hence, this Unified Multiset Simulation Paradigm (UMSP) can be used for all conventional algorithms [15], Tabu search, Markov chain Monte Carlo (MCMC), Particle Filters [6], Evolutionary algorithms-classifier systems, bucket brigade learning , Genetic algorithms and Programming [14], Immunocomputing, Self-organized criticality [4] and Active Walker models (ants with scent or multiwalkerparadigm where each walker can influence the other through a shared landscape based on probabilistic selection [9], and Biomimicry [16]. Also it is applicable to non-equilibrium systems using oscillatory mechanisms involving catalytic reactionsas for example of producing ATP (Adenosine triphosphate) from ATP [8].…”

Section: Introductionmentioning

confidence: 99%

Simulating Complex Dynamical Systems in a Distributed Programming Environment

Krishnamurthy

2004

Lecture Notes in Computer Science

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Abstract. This paper describes a rule-based generic programming and simulation paradigm, for conventional hard computing and soft and innovative computing e.g., dynamical, genetic, nature inspired self-organized criticality and swarm intelligence. The computations are interpreted as the outcome arising out of deterministic, non-deterministic or stochastic interaction among elements in a multiset object space that includes the environment. These interactions are like chemical reactions and the evolution of the multiset can mimic the evolution of the complex system. Since the reaction rules are inherently parallel, any number of actions can be performed cooperatively or competitively among the subsets of elements. This paradigm permits carrying out parts or all of the computations independently in a distributed manner on distinct processors and is eminently suitable for cluster and grid computing.

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Mathematical Models of Synaptic Transmission and Short-Term Plasticity

Bertram¹

2005

Lecture Notes in Mathematics

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Mathematical Theory of Nonequilibrium Steady States

Cited by 239 publications

References 0 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

Simulating Complex Dynamical Systems in a Distributed Programming Environment

Mathematical Models of Synaptic Transmission and Short-Term Plasticity

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