Non equilibrium steady states : fluctuations and large deviations of the density and of the current

Bernard Derrida (1, 2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 LPS - Laboratoire de Physique Statistique de l'ENS

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.

Domaines: Physique [physics]

Bernard Derrida. Non equilibrium steady states : fluctuations and large deviations of the density and of the current. Journal of Statistical Mechanics: Theory and Experiment, 2007, 2007 (07), pp.P07023-P07023. ⟨10.1088/1742-5468/2007/07/P07023⟩. ⟨hal-03285579⟩