Dynamical equivalence classes for Markov jump processes

TL;DR

This paper introduces the concept of dynamical equivalence classes for continuous-time Markov jump processes, showing how different processes can have identical current fluctuations despite driven out of equilibrium.

Contribution

It extends the notion of dynamical equivalence classes from discrete-time Markov chains to continuous-time processes using rate matrix symmetries.

Findings

Dynamical equivalence classes are characterized by the symmetric part of rate matrices.

The skew-symmetric part of the rate matrix allows for different splittings of thermodynamic forces.

Processes within the same class exhibit identical current fluctuations in the stationary state.

Abstract

Two different Markov jump processes driven out of equilibrium by constant thermodynamic forces may have identical current fluctuations in the stationary state. The concept of dynamical equivalence classes emerges from this statement as proposed by Andrieux for discrete-time Markov chains on simple graphs. We define dynamical equivalence classes in the context of continuous-time Markov chains on multigraphs using the symmetric part of the rate matrices that define the dynamics. The freedom on the skew-symmetric part is at the core of the freedom inside a dynamical equivalence class. It arises from different splittings of the thermodynamic forces onto the system's transitions.