2021/10/30 by Manh Hong Duong, Duong, Manh Hong, Michela Ottobre +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics and Entropy #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2111.00286
openalex publication_date 2021/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two approaches to study non-reversible Markov processes, namely the Hypocoercivity Theory (HT) and GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling); the basic idea behind both of them is to split the process into a reversible component and a non-reversible one, and then quantify the way in which they interact. We compare such theories and provide explicit formulas to pass from one formulation to the other; as a bi-product we give a simple proof of the link between reversibility of the dynamics and gradient flow structure of the associated Fokker-Planck equation. We do this both for linear Markov processes and for a class of nonlinear Markov process as well. We then characterize the structure of the Large deviation functional of generalised-reversible processes; this is a class of non-reversible processes of large relevance in applications. Finally, we show how our results apply to two classes of Markov processes, namely non-reversible diffusion processes and a class of Piecewise Deterministic Markov Processes (PDMPs), which have recently attracted the attention of the statistical sampling community. In particular, for the PDMPs we consider we prove entropy decay.