Entropy of non-equilibrium stationary measures of boundary driven TASEP

Cedric Bernardin (1) , Patricia Gonçalves (2, 3) , Claudio Landim (4, 5)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 PUC-Rio - Departamento de Informática = Department of Informatics
3 CMAT - Centro de Matemática [Minho]
4 IMPA - Instituto Nacional de Matemática Pura e Aplicada
5 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Mots clés: boundary driven asymmetric exclusion processes; Non-equilibrium stationary states; phase transitions; large deviations; quasipotential; boundary driven asymmetric exclusion processes.

Domaines: Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Cedric Bernardin, Patricia Gonçalves, Claudio Landim. Entropy of non-equilibrium stationary measures of boundary driven TASEP. Journal of Statistical Physics, 2013. ⟨hal-00911122⟩