# Thermodynamics of accelerated fermion gas and instability at Unruh temperature

## TL;DR

This paper explores the thermodynamics of an accelerated fermion gas, revealing a duality between quantum statistical and geometrical approaches, and identifies an instability at the Unruh temperature with potential implications for heavy-ion physics.

## Contribution

It introduces a novel connection between the energy density of accelerated fermion gases and quantum corrections in curved spacetime, highlighting a discontinuity at the Unruh temperature.

## Key findings

- Discontinuity in energy density at T=TU
- Negative energy density for T<TU indicating instability
- Duality between quantum statistical and geometrical approaches

## Abstract

We demonstrate that the energy density of an accelerated fermion gas evaluated within quantum statistical approach in Minkowski space is related to a quantum correction to the vacuum expectation value of the energy-momentum tensor in a space with non-trivial metric and conical singularity. The key element of the derivation is the existence of a novel class of polynomial Sommerfeld integrals. The emerging duality of quantum statistical and geometrical approaches is explicitly checked at temperatures $T$ above or equal to the Unruh temperature $T_U$. Treating the acceleration as an imaginary part of the chemical potential allows for an analytical continuation to temperatures $T<T_U$ . There is a discontinuity at $T=T_U$ manifested in the second derivative of the energy density with respect to the temperature. Moreover, energy density becomes negative at $T<T_U$, apparently indicating some instability. Obtained results might have phenomenological implications for the physics of heavy-ion collisions.