Casimir entropy and nonlocal response functions to the off-shell quantum fluctuations

TL;DR

This paper investigates how nonlocal response functions to quantum fluctuations affect the Casimir free energy and entropy at low temperatures, resolving thermodynamic inconsistencies in the Lifshitz theory.

Contribution

It introduces an alternative nonlocal response approach that aligns the Lifshitz theory with thermodynamic principles, especially the Nernst heat theorem.

Findings

Casimir entropy remains positive and approaches zero at low temperatures.

The nonlocal response accounts for electron dissipation effects.

The approach resolves the Casimir puzzle related to thermodynamic violations.

Abstract

The nonlocal response functions to quantum fluctuations are used to find asymptotic expressions for the Casimir free energy and entropy at arbitrarily low temperature in the configuration of two parallel metallic plates. It is shown that by introducing an alternative nonlocal response to the off-the-mass-shell fluctuations the Lifshitz theory is brought into agreement with the requirements of thermodynamics. According to our results, the Casimir entropy calculated using the nonlocal response functions, which take into account dissipation of conduction electrons, remains positive and monotonously goes to zero with vanishing temperature, i.e., satisfies the Nernst heat theorem. This is true for both plates with perfect crystal lattices and for lattices with defects of structure. The obtained results are discussed in the context of the Casimir puzzle.