By Berezin F.

''I learn this lecture direction in 1966–67 on the division of Mechanics and arithmetic of the Moscow kingdom collage. presently statistical physics is greater than ninety% heuristic technological know-how. which means the evidence confirmed during this technology are usually not proved, typically, within the mathematical that means of this note even supposing the arguments resulting in them are particularly convincing.'' - F. Berezin, 1972

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1) For example, assume that Ω is a room. § 8. 1. The typical graph of v(q) The assumption on potential implies an important corollary: There exists a constant C independent of n such that n i,j=1 v(xi − xj ) ≥ nC for any points xi . 2. The small and grand ensembles. In order to enter the realm of ideas of statistical physics we should subdivide the system into weakly interacting subsystems. Let us discuss how one can do it. Denote the system considered by C and its phase space by L. Subdivide the volume Ω into a large number K of macroscopic non-interacting subvolumes Ωα 2) .

The intermediary stage seems to be unjustiﬁed. This is due to the fact that our intuition automatically takes into account the principle of indistinguishability of particles. The principle of indistinguishability of the particles. Let the dynamical system consist of N non-interacting identical subsystems. In this case, the states of the system which are obtained from each other by permutation of coordinates (p(α) , q (α) ) of the subsystems are indistinguishable. The precise meaning of the word“indistinguishable” is that all the physical quantities at our disposal are symmetric with respect to the permutations of the coordinates of the subsystems 10) and therefore assume the same values at the points with interchanged coordinates.

12) led us to the situation when the Gibbs distribution takes place. 14) we obtain as a result of the 1-st thermodynamic passage to the limit that F= f (p1 , q1 , . . 8) and N H= i=1 p2i + 2m 1≤i