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We develop fluctuational electrodynamics for media with nonlinear opticalresponse in and out of thermal equilibrium. Starting from the stochasticnonlinear Helmholtz equation and using the fluctuation dissipation theorem, weobtain perturbatively a deterministic nonlinear Helmholtz equation for theaverage field, the physical linear response, as well as the fluctuations andRytov currents. We show that the effects of nonlinear optics, in or out ofthermal equilibrium, can be taken into account with an effective, system-awaredielectric function. We discuss the heat radiation of a planar, nonlinearsurface, showing that Kirchhoff's must be applied carefully. We find that thespectral emissivity of a nonlinear nanosphere can in principle be negative,implying the possibility of heat flow reversal for specific frequencies.

Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium