Ensemble dependence of information-theoretic contributions to the entropy production

TL;DR

This paper explores how the decomposition of entropy production into information-theoretic contributions varies depending on the initial state of the environment, extending previous results beyond thermal baths.

Contribution

It generalizes the entropy production decomposition to non-thermal initial states of the environment, showing the dependence of contributions on the initial ensemble.

Findings

Entropy production can be expressed as a sum of mutual information and displacement terms.

The relative weights of these contributions depend on the environment's initial state.

Different initial states with the same reduced dynamics yield different information-theoretic contributions.

Abstract

The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.