Low temperature Casimir-Lifshitz free energy and entropy: the case of poor conductors

TL;DR

This paper investigates the low-temperature behavior of Casimir-Lifshitz free energy and entropy for poor conductors, addressing theoretical controversies and proposing a formalism for systems without thermodynamic anomalies.

Contribution

It develops a general formalism for calculating low-temperature Casimir free energy corrections in poor conductors modeled with Drude permittivity.

Findings

Calculated low-temperature free energy for poor conductors.

Analyzed violations of Nernst's heat theorem in Casimir thermodynamics.

Provided insights into temperature corrections for semiconducting materials.

Abstract

The controversy concerning the temperature correction to the Casimir force has been ongoing for almost a decade with no view to a solution and has recently been extended to include semiconducting materials. We review some theoretical aspects of formal violations of Nernst's heat theorem in the context of Casimir Lifshitz thermodynamics and the role of the exponent of the leading term of the dielectric permittivity with respect to imaginary frequency. A general formalism for calculating the temperature corrections to free energy at low temperatures is developed for systems which do not exhibit such anomalies, and the low temperature behaviour of the free energy in a gap between half-spaces of poorly conducting materials modelled with a Drude type permittivity is calculated.