## Continuous functions of molecular distributions

The problem of constructing a statistical theory of equilibrium systems is the establishment of general expressions for statistical distributions, i.e., such distributions when the averages calculated with their help correspond to the observed macroscopic quantities that appear in thermodynamic relationships. Starting with [2], the calculations were constructed by direct averaging of the characteristics using the Gibbs distribution function wN (r1, …, rN). This path is convenient for weakly interacting particles. More general and fruitful was the approach to the theory of non-ideal statistical systems, developed by N.N. Bogolyubov [6,16]. It is based on the idea of investigating not the integral value of the partition function Q = Q(T, V, N), but the correlation properties of the particles of the system expressed in terms of the corresponding correlation functions. This makes it possible not to calculate the infinite-dimensional integral Q in the forehead, but to solve a system of several integrodifferential equations for the correlation functions. The idea has acquired such a general significance in statistical mechanics that it embraced not only the theory of non-ideal equilibrium systems, but also the kinetic theory.