# The second law of thermodynamics at the microscopic scale

## TL;DR

This paper explores how the second law of thermodynamics applies at the microscopic quantum level, focusing on energy-preserving interactions and the emergence of equilibrium states.

## Contribution

It demonstrates the validity of the second law in quantum systems through analysis of energy-conserving interactions and equilibrium state formation.

## Key findings

- Equilibrium states are typical in entangled quantum systems.
- Relaxation to equilibrium occurs without significant energy exchange.
- The second law holds at the microscopic quantum scale.

## Abstract

In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this paper, we investigate how the relaxation toward equilibrium is made possible through interactions that do not lead to significant exchange of energy, and argue for the validity of the second law of thermodynamics at the microscopic scale.