Entropy Production for Discrete-Time Markov Processes

TL;DR

This paper reviews various definitions of entropy production in discrete-time Markov processes, clarifies their relationships, and evaluates their properties and applicability through theoretical analysis and numerical examples.

Contribution

It provides a comprehensive comparison of multiple entropy production definitions for discrete-time Markov processes, including their properties and conditions for equivalence.

Findings

All definitions satisfy non-negativity of entropy production.

Inequalities between total and marginal entropy production depend on the definition.

Numerical calculations confirm the theoretical distinctions among definitions.

Abstract

We study the multiple definitions of the entropy production for discrete-time Markov processes in single systems and composite systems. These definitions have been studied in single systems, but less so in composite systems. With a clear distinction, we review the equivalence condition and the meaning of the multiple definitions and show that all definitions satisfy the important property for the entropy production, such as non-negativity. We also show that the inequalities between total entropy production and marginal entropy production holds for a definition but doesn't for another definition. Furthermore, we verify that fact by calculating entropy productions for Gaussian process and numerically show the result. Finally, we find appropriate use of each definition taking all results into account.