Maximal temperature in a simple thermodynamical system

TL;DR

The paper demonstrates that in a simple thermodynamical system obeying quantum mechanics and classical gravity, there exists a maximal temperature around three times lower than the Planck temperature, beyond which black holes dominate.

Contribution

It introduces the concept of a maximal temperature in thermodynamical systems due to black hole formation before quantum gravity effects become relevant.

Findings

Maximal temperature is about three times lower than the Planck temperature.

Black hole formation dominates the system at the critical temperature.

The maximal temperature is derived from classical gravity considerations.

Abstract

Temperature in a simple thermodynamical system is not limited from above. It is also widely believed that it does not make sense talking about temperatures higher than the Planck temperature in the absence of the full theory of quantum gravity. Here, we demonstrate that there exist a maximal achievable temperature in a system where particles obey the laws of quantum mechanics and classical gravity before we reach the realm of quantum gravity. Namely, if two particles with a given center of mass energy come at the distance shorter than the Schwarzschild diameter apart, according to classical gravity they will form a black hole. It is possible to calculate that a simple thermodynamical system will be dominated by black holes at a critical temperature which is about three times lower than the Planck temperature. That represents the maximal achievable temperature in a simple thermodynamical system.