Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces

Noé Cuneo (1, 2) , 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 establish the Level-1 and Level-3 Large Deviation Principle (LDP) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which thermody-namic formalism does not apply. Such decoupling conditions arise naturally in multifractal analysis, in Gibbs states with hard-core interactions, and in the statistics of repeated quantum measurement processes. We also prove the LDP for the entropy production of pairs of such measures and derive the related Fluctuation Relation. The proofs are based on Ruelle–Lanford functions, and the exposition is essentially self-contained.

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

Noé Cuneo, Vojkan Jakšić, Claude-Alain Pillet, Armen Shirikyan. Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces. 2017. ⟨hal-01672683v1⟩