Entropy production and the arrow of time

TL;DR

This paper establishes an exact link between entropy production and the distinguishability of a process from its time-reversal, applicable to various initial conditions and both classical and quantum systems.

Contribution

It introduces a universal relationship connecting entropy production with the relative entropy between forward and backward states, valid across multiple initial distributions and system types.

Findings

The relationship holds for classical and quantum systems.

It applies to various initial conditions like canonical and grand canonical.

Provides a unified framework for understanding entropy and time asymmetry.

Abstract

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid for a wide family of initial conditions, such as canonical, constrained canonical, multi-canonical and grand canonical distributions, as well as both for classical and quantum systems.