# Entropy production and time-asymmetry in the presence of strong interactions

## TL;DR

This paper extends the understanding of entropy production and time-asymmetry to strongly coupled non-equilibrium systems, showing that equilibrium concepts can be generalized beyond weak coupling and providing a framework for experimental verification.

## Contribution

It introduces a generalized framework for entropy production in strongly coupled systems, including a conditional equilibrium state concept and a generalized Crooks relation.

## Key findings

- Entropy production quantifies deviation from conditional equilibrium.
- The stochastic entropy production satisfies a generalized Crooks relation.
- Results extend weak coupling thermodynamics to strong coupling regimes.

## Abstract

It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework to a more general class of non-equilibrium states, we show that the equilibrium properties of the bath can be well-defined, even when the system is arbitrarily far from equilibrium and correlated with the bath. These states, which retain a notion of temperature, take the form of conditional equilibrium distributions. For out-of-equilibrium processes we show that the average entropy production quantifies the extent to which the system-bath state is driven away from the conditional equilibrium distribution. In addition, we show that the stochastic entropy production satisfies a generalised Crooks relation and can be used to quantify time-asymmetry of correlated non-equilibrium processes. These results naturally extend the familiar properties of entropy production in weakly-coupled systems to the strong coupling regime. Experimental measurements of the entropy production at strong coupling could be pursued using optomechanics or trapped ion systems, which allow strong coupling to be engineered.