2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113387We 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.4 pages, 2 figures. Published version, revised and more detailedStatistical MechanicsSoft Condensed MatterQuantum Physicstext