Thermodynamic properties of neutral Dirac particles in the presence of an electromagnetic field

TL;DR

This paper analyzes the thermodynamic behavior of neutral Dirac particles under electromagnetic influence, comparing relativistic and non-relativistic regimes, and finds key differences in energy and heat capacity.

Contribution

It provides a detailed comparison of thermodynamic functions for neutral Dirac particles in electromagnetic fields, highlighting relativistic effects and the impact of electric fields.

Findings

Relativistic mean energy and heat capacity are twice those of non-relativistic cases.

Helmholtz free energy and entropy increase with electric field strength.

Magnetic field has no effect on thermodynamic functions.

Abstract

In this paper, we investigate the thermodynamic properties of a set of neutral Dirac particles in the presence of an electromagnetic field in contact with a heat bath for the relativistic and non-relativistic cases. In order to perform the calculations, the high-temperature limit is considered and the Euler-MacLaurin formula is taking into account. Next, we explicitly determine the behavior of the main thermodynamic functions of the canonical ensemble: the Helmholtz free energy, the mean energy, the entropy, and the heat capacity. As a result, we verified that the mean energy and the heat capacity for the relativistic case are two times the values of the non-relativistic case, thus, satisfying the so-called Dulong-Petit law. In addition, we also verified that the Helmholtz free energy and the entropy in both cases increase as a function of the electric field. Finally, we note that there exists no influence on the thermodynamic functions due to the magnetic field.