Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces
Mathematical Physics
2019-06-28 v3 Statistical Mechanics
Dynamical Systems
math.MP
Probability
Abstract
We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic 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.
Cite
@article{arxiv.1712.09038,
title = {Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces},
author = {Noé Cuneo and Vojkan Jakšić and Claude-Alain Pillet and Armen Shirikyan},
journal= {arXiv preprint arXiv:1712.09038},
year = {2019}
}