# Microscopic theory for the time irreversibility and the entropy production

## TL;DR

This paper develops a microscopic theoretical framework linking irreversibility and entropy production in stochastic thermodynamics, considering the entire system including environment, and illustrates it with a charged particle example.

## Contribution

It derives a relation between irreversibility and entropy production from deterministic equations, considering the whole system and environment, under the Markov approximation.

## Key findings

- Provides a guideline for choosing the proper reverse process.
- Derives the relation starting from deterministic equations.
- Demonstrates with a charged particle in a magnetic field.

## Abstract

In stochastic thermodynamics, the entropy production of a thermodynamic system is defined by the irreversibility measured by the logarithm of the ratio of the path probabilities in the forward and reverse processes. We derive the relation between the irreversibility and the entropy production starting from the deterministic equations of motion of the whole system consisting of a physical system and a surrounding thermal environment. The physical system is driven by a nonconservative force. The derivation assumes the Markov approximation that the environmental degrees of freedom equilibrate instantaneously. Our approach concerns the irreversibility of the whole system not only the irreversibility of the physical system only. This approach provides a guideline for the choice of the proper reverse process to a given forward process. We demonstrate our idea with an example of a charged particle in the presence of a time-varying magnetic field.