Classical limit of the Casimir entropy for scalar massless field

TL;DR

This paper investigates the finite-temperature Casimir effect for a massless scalar field between parallel plates in multiple dimensions, revealing that entropy's sign, influenced by boundary conditions, dictates the Casimir force's nature.

Contribution

It provides a comprehensive analysis of the Casimir entropy's behavior under various boundary conditions in multiple dimensions, highlighting its geometric dependence.

Findings

Entropy sign determines Casimir force direction.

Boundary conditions influence entropy and force.

Geometrical factors govern thermodynamic properties.

Abstract

We study the Casimir effect at finite temperature for a massless scalar field in the parallel plates geometry in N spatial dimensions, under various combinations of Dirichlet and Neumann boundary conditions on the plates. We show that in all these cases the entropy, in the limit where energy equipartitioning applies, is a geometrical factor whose sign determines the sign of the Casimir force.