Fluctuation Theorem and Thermodynamic Formalism
Abstract
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.
Cite
@article{arxiv.1712.05167,
title = {Fluctuation Theorem and Thermodynamic Formalism},
author = {Noé Cuneo and Vojkan Jakšić and Claude-Alain Pillet and Armen Shirikyan},
journal= {arXiv preprint arXiv:1712.05167},
year = {2026}
}
Comments
Added references and a note clarifying the status of this preprint in 2026: most of its content is now part of a recent monograph by the same authors, and the open question raised in Remark 6.6 has since been settled by one of the authors, rendering some parts of the proofs superfluous, although technically correct. Fixed minor typos