Entropy of non-equilibrium stationary measures of boundary driven TASEP

Creators: Bernardin, Cedric; Gonçalves, Patricia; Landim, Claudio

Others:: Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); Departamento de Informática (PUC-Rio) ; Pontifical Catholic University of Rio de Janeiro (PUC); Centro de Matemática [Minho] (CMAT) ; Universidade do Minho = University of Minho [Braga]; Instituto Nacional de Matemática Pura e Aplicada (IMPA) ; Instituto Nacional de matematica pura e aplicada; Laboratoire de Mathématiques Raphaël Salem (LMRS) ; Université de Rouen Normandie (UNIROUEN) ; Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)

Description

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state converges to the Gibbs- Shannon entropy of the local equilibrium state. Moreover, we prove that its fluctuations are Gaussian, except when the mean displacement of particles produced by the bulk dynamics agrees with the particle flux induced by the density reservoirs in the maximal phase regime.

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Entropy of non-equilibrium stationary measures of boundary driven TASEP

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