Ja n 20 04 Some Implications of the Density Matrix Deformation in Statistical Mechanics of the Early

This work is an extension of the study into statistical mechanics of the early Universe that has been the subject in prior works of the author, the principal approach being the density matrix deformation. In the work it is demonstrated that the previously derived exponential ansatz may be successfully applied to the derivation of the free and average energy deformation as well as entropy deformation. Based on the exponential ansatz, the derivation of a statistical-mechanical Liouville equation as a deformation of the quantum-mechanical counterpart is presented. It is shown that deformed Liouville equation will possess nontrivial components as compared to the normal equation in two cases: for the original sin-gularity (i.e. early Universe) and for black hole, that is in complete agreement with the results obtained by the author with coworkers in earlier works devoted to the deformation in quantum mechanics at Planck scale. In conclusion some possible applications of the proposed methods are given, specifically for investigation into ther-modynamics of black holes.