The Boltzmann distribution function for equilibrium fluctuations

A complex of issues related to the problem proving Boltzmann formula for probability density (distribution) w(η) values a certain set parameters η an equilibrium system is investigated. The classical expresses this distribution through non-equilibrium free energy F (η) , which depends on mentioned parameters. This possible because after occurrence fluctuations, finds itself in state, evolves further equilibrium. specified are chosen according under consideration. In theory phase transitions, they called order Questions consideration include definition and construction w(η ) it microscopic theory. approaches Landau, Leontovich, Peletminsky discussed. It proposed investigate results states vicinity leading ideas research considering state as being realized presence appropriate external field, using Gibbs entropy, applying system. article continuation authors' works sets task clarifying some their statements well simplifying calculations. Among other things, following discussed: expansion powers simplification calculation, normalization approximate expressions possibilities studying our expression effective Landau Hamiltonian, refinement calculation spatially inhomogeneous system, investigation new types interactions with Hamiltonian.