Macroscopic theory of electromagnetic fluctuations and stationary radiative heat transfer

For the macroscopic description of thermal electromagnetic fluctuations two methods are frequently used: (i) linear-response theory and the fluctuation-dissipation theorem (FDT of the first kind) and (ii) Langevin theory, i.e., stochastic electrodynamics (FDT of the second kind). The two methods are compared. The identity of both theories in global thermal equilibrium is proven. This identity is expressed by relations between the imaginary and real parts of the Green functions on the one side and volume integrations over products of two Green functions on the other side. The correct treatment of infinitely extended vacuum regions with respect to these integrations is discussed. The local interpretation of the two methods in open systems leads to different results: The Poynting vector calculated by the FDT of the first kind vanishes identically, whereas the FDT of the second kind results in a nonvanishing radiative heat transfer. The basic assumptions which are responsible for the different results are extensively discussed. Simple examples are dealt with to make contact with the phenomenological theory of radiative heat transfer.