Housekeeping Entropy in Continuous Stochastic Dynamics with Odd-Parity Variables

TL;DR

This paper explores the detailed decomposition of entropy production in continuous stochastic systems with odd-parity variables, revealing multiple ways to split housekeeping entropy and their relation to detailed balance and parity symmetry.

Contribution

It introduces a novel, parameterized decomposition of housekeeping entropy in continuous systems with odd-parity variables, extending previous discrete-variable results.

Findings

Multiple entropy decomposition methods characterized by a parameter {}

One part of the housekeeping entropy satisfies the fluctuation theorem

The other part relates to parity asymmetry of the stationary distribution

Abstract

We investigate the decomposition of the total entropy production in continuous stochastic dynamics when there are odd-parity variables that change their signs under time reversal. The first component of the entropy production, which satisfies the fluctuation theorem, is associated with the usual excess heat that appears during transitions between stationary states. The remaining housekeeping part of the entropy production can be further split into two parts. We show that this decomposition can be achieved in infinitely many ways characterized by a single parameter {\sigma}. For an arbitrary value of {\sigma}, one of the two parts contributing to the housekeeping entropy production satisfies the fluctuation theorem. We show that for a range of {\sigma} values this part can be associated with the breakage of the detailed balance in the steady state, and can be regarded as a continuous version of the corresponding entropy production that has been obtained previously for discrete state variables. The other part of the housekeeping entropy does not satisfy the fluctuation theorem and is related to the parity asymmetry of the stationary state distribution. We discuss our results in connection with the difference between continuous and discrete variable cases especially in the conditions for the detailed balance and the parity symmetry of the stationary state distribution.