Fluctuation Theorem and Thermodynamic Formalism

Théorème de fluctuation et formalisme thermodynamique

Noé Cuneo (1) , Vojkan Jakšić (2) , Claude-Alain Pillet (3, 4) , Armen Shirikyan (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 Department of Mathematics and Statistics [Montréal]
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 7332

We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we establish the FT in the phase transition regime. These results hold under minimal chaoticity assumptions (expansiveness and specification) and require no ergodicity conditions. They are also valid for systems that are not necessarily invertible and involutions other than time reversal. Further extensions involve asymptotically additive potential sequences and the corresponding weak Gibbs measures. The generality of these results allows to view the FT as a structural facet of the thermodynamic formalism of dynamical systems.

Mots clés: chaotic dynamical systems; entropy production; fluctuation theorem; fluctuation relation; large deviations; periodic orbits; Gibbs measures; non-equilibrium statistical mechanics

Domaines: Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]; Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Noé Cuneo, Vojkan Jakšić, Claude-Alain Pillet, Armen Shirikyan. Fluctuation Theorem and Thermodynamic Formalism. 2017. ⟨hal-01666028⟩