  In this work the Quantum and Statistical Mechanics of the Early Universe,
i.e. at Planck scale, is considered as a deformation of the well-known
theories. In so doing the primary object under deformation in both cases is the
density matrix. It is demonstrated that in construction of the deformed quantum
mechanical and statistical density matrices referred to as density pro-matrices
there is a complete analog. The principal difference lies in a nature of the
deformation parameter that is associated with the fundamental length in the
first case and with a maximum temperature in the second case. Consideration is
also given to some direct consequences, specifically the use of the explicitly
specified exponential ansatz in the derivation from the basic principles of a
semiclassical Bekenstein-Hawking formula for the black hole entropy and of the
high-temperature complement to the canonical Gibbs distribution.
