Entropy Production by Logarithmic Decomposition

TL;DR

This paper introduces a logarithmic decomposition method for dynamics in statistical physics, allowing a systematic and intuitive breakdown of entropy production into symmetric and asymmetric components, clarifying their physical origins.

Contribution

It presents a novel log-decomposition technique of the time evolution operator, enabling clear separation of non-adiabatic and adiabatic entropy production.

Findings

Decomposition of path probability into symmetric and asymmetric parts.

Derivation of non-adiabatic entropy from symmetric operator.

Derivation of adiabatic entropy from asymmetric factor.

Abstract

In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which time evolution operator is logarithmically decomposed into a symmetric operator and an asymmetric factor. Path probability and path entropy production are also systematically and intuitively decomposed into symmetric and asymmetric parts. From symmetric operator, non-adiabatic entropy production is derived, whereas adiabatic entropy production is from asymmetric factor.