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Non-extensive thermodynamics of the radiation in heterogeneous thermal plasmas

Thermodynamic characteristics of the radiation of condensed combustion products presented in the form of agglomerates of metal-oxide nanoparticles demonstrate deviations from the classical Planck's law. We propose to interpret these deviations in terms of the non-additive entropy of the photon system interacting with the heterogeneous combustion products, which makes it possible to use the non-extensive Tsallis thermodynamics for their description. It is assumed that the non-additive character of the radiation entropy in heterogeneous plasma can be explained by the influence of long-range interactions and non-equilibrium physicochemical processes. An expression is obtained for the energy-dependent distribution of the photon density, based on the phenomenological parameter of non-extensiveness $q$ which, in the first approximation, does not depend on the energy. In this case, the "non-extensive" Planck's law can be reduced to the "usual" Planck distribution by introducing the "effective temperature" that exceeds the real temperature. Numerical modelling has shown that the spectral density of photons, the position and magnitude of its maximum depend on the value of the parameter $q$, which can be used for its experimental determination and revelation of its physical nature and origin.