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Linear response relations in fluctuational electrodynamics

Near field radiative heat transfer and dynamic Casimir forces are just two instances of topics of technological and fundamental interest studied via the formalism of fluctuational electrodynamics. From the perspective of experiment and simulations, it is hard to precisely control and probe such non-equilibrium situations. Fluctuations in equilibrium are easier to measure, and can typically be related to non-equilibrium response functions by Green-Kubo relations. We consider a collection of arbitrary objects in vacuum, perturbed by changing the temperature or velocity of one object. Developing a method for computation of higher order correlation functions in fluctuational electrodynamics, we explicitly compare linear response and equilibrium fluctuations. We obtain a Green-Kubo relation for the radiative heat transfer, as well as a closed formula for the vacuum friction in arbitrary geometries in the framework of scattering theory. We comment on the signature of the radiative heat conductivity in equilibrium fluctuations.