# Extensivity, entropy current, area law and Unruh effect

## TL;DR

This paper develops a general method to determine the entropy current in relativistic quantum systems at local equilibrium, demonstrating its extensivity and connection to entanglement entropy in accelerated frames.

## Contribution

It introduces a universal approach to compute the entropy current in relativistic quantum thermodynamics and links it to entanglement entropy in accelerated systems.

## Key findings

- Entropy current exists under certain conditions.
- Logarithm of the partition function is extensive.
- Entanglement entropy corresponds to the integral of the entropy current in Rindler space.

## Abstract

We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying eigenvector is non-degenerate, it is proved that, in general, the logarithm of the partition function is extensive, meaning that it can be expressed as the integral over a 3D space-like hypersurface of a vector current, and that an entropy current exists. We work out a specific calculation for a non-trivial case of global thermodynamic equilibrium, namely a system with constant comoving acceleration, whose limiting temperature is the Unruh temperature. We show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy.