2017/12/14 by Noé Cuneo, Cuneo, Noé, Vojkan Jakšić +5
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #37A30 #37A50 #37A60 #37B10 #37D35 #47A35 #54H20 #60F10 #82C05 #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1712.05167
openalex publication_date 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.