Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

By Lorenzo Bertini, A. Sole, D. Gabrielli, Giovanni Jona-Lasinio, Claudio Landim. 2005

171 citations recorded by the source corpus.

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional I. We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c1aeb98d2f36be3a8862260ecaf28189a8dc1c5f

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Macroscopic fluctuation theory (2014, methodology): “This equation is interpreted as a Hamilton-Jacobi equation (Bertini et al., 2001). As shown in Bertini et al. (2002), V is the maximal positive solution to Eq.”
Non-equilibrium steady states: fluctuations and large deviations of the density and of the current (2007, background): “One can write from (92) (after an integration by part and using the fact that U(0) = U(1) = 0 if ρ(0) = ρa and ρ(1) = ρb) the equation satisfied by U ′(x) ∫ 1 0 dx [( Dρ′ σ − U ′ )2 − ( Dρ′ σ )2] σ 2 = 0 (96) which is the Hamilton-Jacobi [41] equation of Bertini et al. For general D(ρ) and σ(ρ) one ”
Large deviations of the empirical flow for continuous time Markov chains (2012, background): “(ii) In the context of hydrodynamic scaling limits the LDP of the current has been analyzed in [4,5,8,9].”
Principles of maximum entropy and maximum caliber in statistical physics (2013, methodology): “…flux or current also were used to construct distributions and describe fluctuations away from equilibrium (Derrida and Lebowitz, 1998; Maes, 1999; Bodineau and Derrida, 2004; Depken and Stinchcombe, 2004; Bertini et al., 2006; Bodineau and Derrida, 2007; Derrida, 2007; Hurtado and Garrido, 2009).”
Stochastic interacting particle systems out of equilibrium (2007, background): “Referring to [39, 49, 50] for periodic boundary conditions and to [3, 7, 26, 27] for open systems, we here state the law of large numbers, as N → ∞, of”