Application of the Theory of Orlicz Spaces to Statistical Mechanics. I. Integral Equations

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Abstract
In this paper it is suggested that there may exist a fundamental relationship between the variables of thermodynamics, the operators associated with certain nonlinear integral equations of statistical mechanics, and the properties of a class of convex functions, called N functions, investigated by Krasnosel'skii and Rutickii. In particular, it is pointed out that the most general theoretical framework within which all these problems can be studied is that provided by the theory of Orlicz spaces. In the first part of our study, presented here, it is shown that the existence of solutions to certain nonlinear integral equations, derived either from the BBKYG hierarchy or from the grand partition function using a variational approach, can be established with some generality. The relationship between our results and those obtained by Ruelle is discussed.

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