  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 singularity (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 thermodynamics
of black holes.
