2007/10/24 by Amir Dembo, Dembo, Amir, Jean-Dominique Deuschel +1
Mathematics · Physics and Astronomy · #60J25 #60J60 #60J75 #60K35 (Secondary) #82C05 (Primary) 82C31 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0710.4394
openalex publication_date 2007/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of "linear response function" in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is, if the initial measure is invariant for the given Markov semi-group, then for any pair of times s