Abstract
In this paper a new approach to investigation of Quantum and Statistical Mechanics of the Early Universe (Planck scale) - density matrix deformation - is proposed. Quantum Mechanics of the Early Universe is chosen as Quantum Mechanics with Fundamental Length. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of well-known Quantum Mechanics. The proposed approach allows to describe dynamics. It is demonstrated that Statistical Mechanics of the Early Universe is a deformation of the conventional Statistical Mechanics. The statistical-mechanics deformation is constructed by analogy to the earlier quantum mechanical results. Some implications of the obtained results are discussed. In particular, the problem of singularity, possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is noted that the obtained results enable the derivation of the Bekenstein-Hawking’s formula for the black hole entropy in a semiclassical approximation in a simple and natural way.
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