The thermal Casimir effect for conducting plates and the Bohr-van Leeuwen theorem

TL;DR

This paper investigates the thermal Casimir force between conducting plates, analyzing how different theoretical prescriptions align with the Bohr-van Leeuwen theorem, highlighting the importance of ohmic dissipation effects.

Contribution

It demonstrates that only models including ohmic dissipation are consistent with the Bohr-van Leeuwen theorem in the context of the thermal Casimir effect.

Findings

Prescriptions with ohmic dissipation satisfy the Bohr-van Leeuwen theorem.

Neglecting ohmic dissipation leads to inconsistency with classical statistical physics.

Highlights the importance of dissipation effects in modeling the thermal Casimir force.

Abstract

We examine recent prescriptions for estimating the thermal Casimir force between two metallic plates from the point of view of their consistency with the Bohr-van Leeuwen theorem of classical statistical physics. We find that prescriptions including the effect of ohmic dissipation satisfy the theorem, while prescriptions that neglect ohmic dissipation do not.