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This chapter is an introduction to the thermodynamics of systems, based on the correlation function formalism, which has been established to determine the thermodynamic properties of simple liquids. The article begins with a preamble describing few general aspects of the liquid state, among others the connection between the phase diagram and the pair potential u(r), on one hand, and between the structure and the pair correlation function g(r), on the other hand. The pair correlation function is of major importance in the theory of liquids at equilibrium, because it is required for performing the calculation of the thermodynamic properties of systems modeled by a given pair potential. Then, the article is devoted to the expressions useful for calculating the thermodynamic properties of liquids, in relation with the most relevant features of the potential, and provides a presentation of the perturbation theory developed in the four last decades. The thermodynamic perturbation theory is founded on a judicious separation of the pair potential into two parts. Specifically, one of the greatest successes of the microscopic theory has been the recognition of the quite distinct roles played by the repulsive and attractive parts of the pair potential in predicting many properties of liquids. Much attention has been paid to the hard-sphere potential, which has proved very efficient as natural reference system because it describes fairly well the local order in liquids. As an example, the Yukawa attractive potential is also mentioned.

Thermodynamic Perturbation Theory of Simple Liquids