Nature and aims of statistical mechanics

Statistical mechanics is the theoretical apparatus with which one studies the properties of macroscopic systems – systems made up of many atoms or molecules – and relates those properties to the system's microscopic constitution. One branch of the subject, called statistical thermodynamics, is devoted to calculating the thermodynamic functions of a system of given composition when the forces of interaction within and between the system's constituent molecules are given or are presumed known. This first chapter is directed toward obtaining the most commonly used formulas of statistical thermodynamics and much of the remainder of the book illustrates their application.

Because the systems to which the theory is applied consist of large numbers of molecules, and are thus systems of a large number of mechanical degrees of freedom, we are not interested in all the details of their underlying microscopic dynamics (and could hardly hope to know them even if we were interested). Instead, it is the systems' macroscopic properties – among which are the thermodynamic functions – that we wish to understand or to calculate, and these are gross averages over the detailed dynamical states. That is the reason for the word “statistical” in the name of our subject.

A prominent feature in the landscape of statistical mechanics is the Boltzmann distribution law, which tells us with what frequency the individual microscopic states of a system of given temperature occur.