On decompositions of non-reversible processes

TL;DR

This paper explores the decomposition of non-reversible Markov processes, focusing on forces, fluxes, and Hamiltonians, revealing non-uniqueness in iso-dissipation forces and proposing various Hamiltonian decompositions.

Contribution

It introduces new insights into the non-uniqueness of iso-dissipation forces and develops multiple Hamiltonian decompositions for Markov processes.

Findings

Iso-dissipation force non-uniqueness linked to duality notions

Development of different Hamiltonian decompositions

Enhanced understanding of forces and fluxes in non-reversible Markov chains

Abstract

Markov chains are studied in a formulation involving forces and fluxes. First, the iso-dissipation force recently introduced in the physics literature is investigated; we show that its non-uniqueness is linked to different notions of duality giving rise to dual forces. We then study Hamiltonians associated to variational formulations of Markov processes, and develop different decompositions for them.