Thermodynamical aspects of fermions in external electromagnetic fields

TL;DR

This paper investigates the thermodynamics of Dirac fermions in external electromagnetic fields, analyzing both finite-time and time-independent perturbations, and introduces methods to compare free and perturbed evolutions, including explicit formulas for relative entropy.

Contribution

It provides new insights into the thermodynamics of Dirac fields under external fields, especially for time-independent perturbations where standard methods fail, and introduces a way to analyze non-equilibrium states.

Findings

Automorphisms describe finite-time perturbations in KMS states.

Comparison of free and perturbed evolutions via smooth switching.

Explicit formula for the relative entropy of gauge invariant quasi-free states.

Abstract

The thermodynamics of Dirac fields under the influence of external electromagnetic fields is studied. For perturbations which act only for finite time, the influence of the perturbation can be described by an automorphism which can be unitarily implemented in the GNS representations of KMS states, a result long known for the Fock representation. For time-independent perturbations, however, the time evolution cannot be implemented in typical cases, so the standard methods of quantum statistical mechanics do not apply. Instead we show that a smooth switching on of the external potential allows a comparison of the free and the perturbed time evolution, and approach to equilibrium, a possible existence of non-equilibrium stationary states (NESS) and Araki's relative entropy can be investigated. As a byproduct, we find an explicit formula for the relative entropy of gauge invariant quasi-free states.