Inverse problem for Planck formula

Abstract

Planck formula is considered as a first moment (average value) of unknown function of electromagnetic energy distribution of black body radiation. In-verse problem for the definition of the unknown function is solved for Gibbs ensemble. The solution needs of ensembles with both absolute temperatures: positive temperature and negative temperature. Such ensembles are the part of more extended class of ensembles with finite energies and finite phase vol-umes. In addition, the absence of Bohr - van Leeuwen paradox is considered for such statistical ensembles.