Vortices in the Two-Dimensional Simple Exclusion Process

Bodineau, Thierry; Derrida, Bernard; Lebowitz, Joel L.

doi:10.1007/s10955-008-9518-y

Cited by 32 publications

(42 citation statements)

References 23 publications

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“…One says that the Markov chain ξ satisfies the logarithmic Sobolev inequality if there exists a constant c LS ∈ (0, +∞) such that for any µ ∈ P(V ) it holds (recall that π(x) > 0 for any 10) where Ent(µ|π) denotes the relative entropy of µ with respect to π.…”

Section: 2mentioning

confidence: 99%

Large deviations of the empirical flow for continuous time Markov chains

Bertini¹,

Faggionato²,

Gabrielli³

2015

Ann. Inst. H. Poincaré Probab. Statist.

170

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Abstract. We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We give a direct proof using tilting and an indirect one by contraction from the empirical process. Résumé.On considère une chaîne de Markov en temps continuà espace d'états denómbrable, et on prouve un principe de grandes déviations commune pour la mesure empirique et le courant empirique, qui représente le nombre total de sauts entre les paires d'états. On donne une preuve directeà l'aide d'un tilting, et une preuve indirecte par contraction,à partir du processus empirique.

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Section: 2mentioning

confidence: 99%

Large deviations of the empirical flow for continuous time Markov chains

Bertini¹,

Faggionato²,

Gabrielli³

2015

Ann. Inst. H. Poincaré Probab. Statist.

170

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“…For s = 0, W K reduces to the evolution operator of the Master equation W for the symmetric simple exclusion process, and this largest eigenvalue (which is 0) as well as the related eigenvector are known. We now present a way of obtaining the large deviation function ψ K , by a perturbative expansion [41,42] in powers of s.…”

Section: A the Cumulants Of The Activity K(t)mentioning

confidence: 99%

“…Therefore for a fixed density ρ of particles, the constant C in (41,44) and the eigenvalue (42) are given, to leading order in…”

Section: B Bethe Ansatz For Kmentioning

confidence: 99%

Universal cumulants of the current in diffusive systems on a ring

et al. 2008

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We calculate exactly the first cumulants of the integrated current and of the activity (which is the total number of changes of configurations) of the symmetric simple exclusion process (SSEP) on a ring with periodic boundary conditions. Our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form, with the same scaling function for both quantities. This scaling function can be understood either by an analysis of Bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim.

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“…Finally, in section IV C, we show that the cumulant generating function of time-averaged current in a simple electric circuit is expressed in terms of the least energy dissipation rate associated with a variational principle that determines the voltage distribution. In this subsection, we express the variational function (66) in terms of entropy production rate. First, the probability current for a given probability density P (x) is written as…”

Section: Remarks On the Variational Function φ F Hmentioning

confidence: 99%

Thermodynamic formula for the cumulant generating function of time-averaged current

Nemoto

Sasa

2011

Phys. Rev. E

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The cumulant generating function of time-averaged current is studied from an operational viewpoint. Specifically, for interacting Brownian particles under non-equilibrium conditions, we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added, where the modified system is characterized by a variational principle. The formula reminds us of Einstein's fluctuation theory in equilibrium statistical mechanics. Furthermore, since the formula leads to the fluctuation-dissipation relation when the linear response regime is focused on, it is regarded as an extension of the linear response theory to that valid beyond the linear response regime. The formula is also related to previously known theories such as the Donsker-Varadhan theory, the additivity principle, and the least dissipation principle, but it is not derived from them. Examples of its application are presented for a driven Brownian particle on a ring subject to a periodic potential.

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Vortices in the Two-Dimensional Simple Exclusion Process

Cited by 32 publications

References 23 publications

Large deviations of the empirical flow for continuous time Markov chains

Large deviations of the empirical flow for continuous time Markov chains

Universal cumulants of the current in diffusive systems on a ring

Thermodynamic formula for the cumulant generating function of time-averaged current

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