2018/09/19 by Alberto Montefusco, Montefusco, Alberto, Mark A. Peletier +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1809.07253
openalex publication_date 2018/09/19 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes, namely the class of Markov processes that satisfy detailed balance and a large-deviation principle. The generalized fluctuation-dissipation theorem characterizes the deterministic limit of such a Markov process as a generalized gradient flow, a mathematical tool to model a purely irreversible dynamics via a dissipation potential and an entropy function: these are expressed in terms of the large-deviation dynamic rate function of the Markov process and its stationary distribution. We exploit the generalized fluctuation-dissipation theorem to develop a new method of coarse-graining and test it in the context of the passage from the diffusion in a double-well potential to the jump process that describes the simple reaction A \rightleftarrows B (Kramers' escape problem).