Negative temperature: further extensions

TL;DR

This paper explores the concept of negative temperatures in relativistic systems, demonstrating their possible existence in the Dirac vacuum and discussing conditions under which such states can be considered equilibrium.

Contribution

It extends the concept of negative temperature to relativistic quantum systems, specifically showing their realization in the Dirac vacuum via PT symmetry.

Findings

Negative temperatures can exist in the Dirac vacuum.

Such negative temperature states can be in thermodynamic equilibrium if they fill the universe.

Negative temperature states are linked to PT-symmetric transformations.

Abstract

This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi and A. Vulpiani, Statistical mechanics of systems with negative temperature, arXiv:2103.12572. The authors suggest that negative absolute temperatures are consistent with equilibrium thermodynamics. This is correct, if the environment also has negative temperature. Otherwise such states represent the transient though maybe long-lived metastable effects. Here we consider the extension of the negative temperatures to the relativistic systems. We show that the negative state is possible in the Dirac vacuum, which is obtained by the $PT$ symmetry transformation from the conventional Dirac sea. If such vacuum with inverse population fills the whole Universe, its thermodynamics determined by negative temperatures becomes equilibrium.