The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics

The long-standing and highly non-trivial problem of calculating the pressure fluctuations in the Gibbs equilibrium statistical mechanics is fully revised. The previous attempts are critically analyzed and it is shown that the application of the ideas by Bogolyubov gives the full and unambiguous solution of this problem. The crucial role is played by the Bogolyubov's idea of quasiaverages (or rather quasidynamic) quantities - specifically, the pressure P and dynamic compressibility Psi. The virtual conjugate field which eliminates the translational invariance of the Hamilton function H in the limit epsilon -> 0 is the singular potential of the impenetrable walls of the container. The general relations for P and Psi in terms of the derivatives of H are obtained and some examples are studied - i.e., the cases of the ideal vs. non-ideal as well as of uniform vs. non- and quasi-uniform (in Euler sense) Hamilton function H describing the given system.