The statistical distribution for the case of an adiabatically isolated body was obtained in the framework of covariant quantum theory and Wick's rotation in the complex time plane. The covariant formulation of the mechanics of an isolated system lies in the rejection of absolute time and the introduction of proper time as an independent dynamic variable. The equation of motion of proper time is the law of conservation of energy. In this case, the energy of an isolated system is an external parameter for the modified distribution instead of temperature.
A theory of the initial state of the universe is proposed within the framework of the Euclidean quantum theory of gravity. The theory is based on a quantum representation in which the action functional is implemented as an operator on the space of wave functionals depending on the 4D space metric and matter fields. The initial construction object is the eigenvalue of the action operator in the area of the Origin of the universe with the given values of the 3D metric and matter fields on the boundary. The wave function of the initial state is plotted as an exponential of this eigenvalue, after a Wick rotation in the complex plane of the radial variable of the Euclidean 4D space. An estimate of the initial radius of the universe is proposed.
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