# Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations

## TL;DR

This paper demonstrates that in small open systems, entropy production mainly results from environmental displacement from equilibrium, not system-environment correlations, challenging common assumptions and supported by numerical evidence.

## Contribution

It reveals that environmental displacement, rather than mutual information, is the primary driver of entropy production in open systems, with bounds established by the Araki-Lieb inequality.

## Key findings

- Entropy production is mainly due to environmental displacement.
- Mutual information contribution is bounded and not time-extensive.
- Numerical calculations confirm the theoretical results.

## Abstract

We show that the entropy production in small open systems coupled to environments made of extended baths is predominantly caused by the displacement of the environment from equilibrium rather than, as often assumed, the mutual information between the system and the environment. The latter contribution is strongly bounded from above by the Araki-Lieb inequality, and therefore is not time-extensive, in contrast to the entropy production itself. We confirm our results with exact numerical calculations of the system-environment dynamics.