Casimir-Lifshitz force out of thermal equilibrium and asymptotic non-additivity

TL;DR

This paper analyzes the Casimir-Lifshitz force between two plates at different temperatures, revealing its behavior at large distances, including non-additivity effects when one body is a rarefied gas.

Contribution

It extends the understanding of thermal non-equilibrium Casimir forces by deriving their asymptotic behavior and identifying non-additivity effects in specific regimes.

Findings

Force reduces to known equilibrium and non-equilibrium limits

Force is non-additive when one body is a rarefied gas

Identifies cross-over regions at large distances

Abstract

We investigate the force acting between two parallel plates held at different temperatures. The force reproduces, as limiting cases, the well known Casimir-Lifshitz surface-surface force at thermal equilibrium and the surface-atom force out of thermal equilibrium recently derived by M. Antezza \emph{et al.}, Phys. Rev. Lett. {\bf 95}, 113202 (2005). The asymptotic behavior of the force at large distances is explicitly discussed. In particular when one of the two bodies is a rarefied gas the force is not additive, being proportional to the square root of the density. Nontrivial cross-over regions at large distances are also identified.