Fluctuations and linear Response

Rytov formalism allows computation of fluctuations in force and heat, both in and out of thermal equilibrium

          

Linear response relates equilibrium fluctuations to responses to small perturbations:

yellow ball Friction coeficient in vacuum at finite temperature

yellow ball Green Kubo relation (explicitly confirmed) provide coefficient of thermal conductivity

yellow ball  Onsager relation (relying of symmetry of mixed expectation values) give

 "Nonequilibrium Fluctuational QED: Heat Radiation, Heat Transfer and Force,"

V. Golyk, M. Krüger, and M. Kardar, Phys. Rev. B 88, 155117 (2013). (offline)