Non-reversible processes: GENERIC, hypocoercivity and fluctuations

Abstract We consider two approaches to study non-reversible Markov processes, namely the hypocoercivity theory and general equations for non-equilibrium reversible–irreversible coupling; basic idea behind both of them is split process into a reversible component one, then quantify way in which they interact. compare such theories provide explicit formulas pass from one formulation other; as bi-product we give simple proof link between reversibility dynamics gradient flow structure associated Fokker–Planck equation. do this linear processes class nonlinear well. characterise large deviation functional generalised-reversible processes; relevance applications. Finally, show how our results apply classes diffusion piecewise deterministic (PDMPs), have recently attracted attention statistical sampling community. In particular, PDMPs prove entropy decay.