Maximum Entropy Production vs. Kolmogorov-Sinai Entropy in a Constrained ASEP Model

Martin Mihelich (1) , Bérengère Dubrulle (1) , Didier Paillard (2, 3) , Corentin Herbert (4)

1 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
2 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
3 CLIM - Modélisation du climat
4 NCAR - National Center for Atmospheric Research [Boulder]

The asymmetric simple exclusion process (ASEP) has become a paradigmatic toy-model of a non-equilibrium system, and much effort has been made in the past decades to compute exactly its statistics for given dynamical rules. Here, a different approach is developed; analogously to the equilibrium situation, we consider that the dynamical rules are not exactly known. Allowing for the transition rate to vary, we show that the dynamical rules that maximize the entropy production and those that maximise the rate of variation of the dynamical entropy, known as the Kolmogorov-Sinai entropy coincide with good accuracy. We study the dependence of this agreement on the size of the system and the couplings with the reservoirs, for the original ASEP and a variant with Langmuir kinetics.

Keywords: maximum entropy production; Kolmogorov-Sinai Entropy; ASEP model

Domains: Physics [physics]

Martin Mihelich, Bérengère Dubrulle, Didier Paillard, Corentin Herbert. Maximum Entropy Production vs. Kolmogorov-Sinai Entropy in a Constrained ASEP Model. Entropy, 2014, 16, pp.1037 - 1046. ⟨10.3390/e16021037⟩. ⟨cea-01384251⟩