# Irreversibility, the time arrow and a dynamical proof of the second law of thermodynamics

## TL;DR

This paper offers a dynamical proof of the second law of thermodynamics, emphasizing irreversibility and the arrow of time through entropy concepts, with applications to quantum spin systems.

## Contribution

It presents a novel dynamical proof of the second law using entropy upper semicontinuity, extending to quantum systems and discussing irreversibility and the time arrow.

## Key findings

- Dynamical proof of the second law established
- Application to quantum spin models demonstrated
- Implications for irreversibility and the arrow of time discussed

## Abstract

We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example is provided by a class of models of quantum spin systems introduced by Emch and Radin. Consequences regarding irreversibility and the time arrow, as well as possible extensions to quantum continuous systems are discussed.