Representations of States of Infinite Systems in Statistical Mechanics

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Abstract
This paper deals with the representation of states of infinite systems in classical statistical mechanics in terms of probability densities,correlation functions, and zero‐density correlation functions. The class of states considered includes equilibrium states treated previously by Ruelle, and is believed to contain low‐density nonequilibrium states as well. The theory is based on Carter's exponential construction for measure spaces, the representations being in terms of functions on the exponential (i.e., union of symmetrized direct powers) of one‐particle phase space. The main result, which establishes the connections between these three representations, essentially extends a result of Ruelle, but is based on L 1 −convergence rather than uniform convergence on compacts.

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