Abstract
We show how to obtain formal solutions of the chain of equations for distribution functions in classical statistical mechanics. These solutions are in the form of complex functional integrals. They are not unique, which fact is a fundamental property of the equations, and the different solutions are recognized by different integration paths in the complex function space. The different manners of integration correspond to different phases, of which some can be identified with the possible physical states. The treatment of the integrals in some cases is also discussed. They are closely related to generalizations of the molecular field approach to the problem. It is also shown that the functional integrals can be written as averages over an external field and that essentially the same form is valid in the quantum‐mechanical case.
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