Entropic fluctuations in Gaussian dynamical systems

Vojkan Jaksic (1) , Claude-Alain Pillet (2, 3, 4) , Armen Shirikyan (5)

1 Department of Mathematics and Statistics [Montréal]
2 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 7332
5 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the non-equilibrium steady state. The entropy production observable of this model is an unbounded function on the phase space, and its large deviation functionals have a surprisingly rich structure. We explore this structure in some detail.

Mots clés: nonequilibrium statistical mechanics; Gaussian dynamical systems; Entropy production

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

Vojkan Jaksic, Claude-Alain Pillet, Armen Shirikyan. Entropic fluctuations in Gaussian dynamical systems. Reports on Mathematical Physics, 2016, 77 (3), pp.335-376. ⟨10.1016/S0034-4877(16)30034-9⟩. ⟨hal-01196999⟩