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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2020

Non-additive large deviations function for the particle densities of driven systems in contact

Résumé

We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained master equation satisfied by the distribution of the numbers of particles in each system. Assuming that this distribution takes for large systems a large deviations form, we obtain the equation (similar to a Hamilton-Jacobi equation) satisfied by the large deviations function of the densities. Depending on the systems considered, this equation may satisfy or not the macroscopic detailed balance property, i.e., a time-reversibility property at large deviations level. In the absence of macroscopic detailed balance, the large deviations function can be determined as an expansion close to a solution satisfying macroscopic detailed balance. In this case, the large deviations function is generically non-additive, i.e., it cannot be split as two separate contributions from each system. In addition, the large deviations function can be interpreted as a non-equilibrium free energy, as it satisfies a generalization of the second law of thermodynamics, in the spirit of the Hatano-Sasa relation. Some of the results are illustrated on an exactly solvable driven lattice gas model.
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Dates et versions

hal-03043340 , version 1 (07-12-2020)

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Jules Guioth, Éric Bertin. Non-additive large deviations function for the particle densities of driven systems in contact. Journal of Statistical Mechanics: Theory and Experiment, 2020, 2020 (6), pp.063209. ⟨10.1088/1742-5468/ab8555⟩. ⟨hal-03043340⟩

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