Large Deviation Functional of the Weakly Asymmetric Exclusion Process

Derrida, Bernard; Enaud, C.

doi:10.1023/b:joss.0000012501.43746.cf

Cited by 85 publications

(134 citation statements)

References 34 publications

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“…5). As expected, the result agrees with the expression obtained using other methods [12,13]. However, the structure of the resulting LDF has not been explored in detail.…”

Section: Macroscopic Fluctuation Theorysupporting

confidence: 87%

Singularities in large deviation functionals of bulk-driven transport models

Aminov¹,

Bunin²,

Kafri³

2014

J. Stat. Mech.

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Abstract. The large deviation functional of the density field in the weakly asymmetric simple exclusion process with open boundaries is studied using a combination of numerical and analytical methods. For appropriate boundary conditions and bulk drives the functional becomes non-differentiable. This happens at configurations where instead of a single history, several distinct histories of equal weight dominate their dynamical evolution. As we show, the structure of the singularities can be rather rich. We identify numerically analogues in configuration space of first order phase transition lines ending at a critical point and analogues of tricritical points. First order lines terminating at a critical point appear when there are configurations whose dynamical evolution is controlled by two distinct histories with equal weight. Tricritical point analogues emerge when there are configurations whose dynamical evolution is controlled by three distinct histories with equal weight. A numerical analysis suggests that the structure of the singularities can be described by a Landau like theory. Finally, in the limit of an infinite bulk bias we identify singularities which arise from a competition of s histories, with s arbitrary. In this case we show that all the singularities can be described by a Landau like theory.Singularities in Large Deviation Functionals of Bulk-Driven Transport Models 2

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“…5). As expected, the result agrees with the expression obtained using other methods [12,13]. However, the structure of the resulting LDF has not been explored in detail.…”

Section: Macroscopic Fluctuation Theorysupporting

confidence: 87%

Singularities in large deviation functionals of bulk-driven transport models

Aminov¹,

Bunin²,

Kafri³

2014

J. Stat. Mech.

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“…By the formula for η t (j) in terms of ξ t (j), and by (3.3), a summation by parts yields that for functions 10) where the remainder R N t (G) is given by…”

Section: A Microscopic Cole-hopf Transformationmentioning

confidence: 99%

Nonequilibrium fluctuations of one-dimensional boundary driven weakly asymmetric exclusion processes

Gonçalves¹,

Landim²,

Milanés³

2017

Ann. Appl. Probab.

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“…With this choice of parameters, at t = 2kπ, we have ρA = 0.75, ρB = 0.25 [30]. The duration of a single trajectory is taken to be t f = 10 · 2π.…”

Section: The Distribution Of Heat Flow In a Markov Processmentioning

confidence: 99%

Work and heat probability distributions in out-of-equilibrium systems

Imparato

Peliti

2007

Comptes Rendus. Physique

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We review and discuss the equations governing the distribution of work done on a system which is driven out of equilibrium by external manipulation, as well as those governing the entropy flow to a reservoir in a nonequilibrium system. We take advantage of these equations to investigate the path phase transition in a manipulated meanfield Ising model and the large-deviation function for the heat flow in the asymmetric exclusion process with periodically varying transition probabilities.

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Large Deviation Functional of the Weakly Asymmetric Exclusion Process

Cited by 85 publications

References 34 publications

Singularities in large deviation functionals of bulk-driven transport models

Singularities in large deviation functionals of bulk-driven transport models

Nonequilibrium fluctuations of one-dimensional boundary driven weakly asymmetric exclusion processes

Work and heat probability distributions in out-of-equilibrium systems

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