The basic elements of statistical thermodynamics were developed in Chapter 2. In this chapter, we digress briefly from development of the statistical theory to expand the theoretical framework using mathematical tools and macroscopic analysis. By doing so we more strongly link the statistical theory to classical thermodynamics and set the stage for alternative statistical viewpoints considered in Chapter 4.

Necessary Conditions for Thermodynamic Equilibrium

In the previous chapter, we have derived several important pieces of information about thermodynamic systems. The goal of this chapter is to expand the framework of macroscopic thermodynamic theory so that it can be applied effectively to a variety of system types. We will begin by summarizing the important ideas developed in the last chapter.

So far, we have taken the volume V, internal energy U, and particle numbers Na and Nb, to be intrinsic properties for any system we may consider. We subsequently defined the properties entropy S, temperature T, pressure P, and chemical potentials µa and µb. Our analysis of the statistical characteristics of thermodynamic systems has led to the conclusion that for a system with fixed U, V, Na, and Nb, equilibrium corresponds to a maximum value of the system entropy. This is referred to as the entropy maximum principle. The entropy of a composite system with an arbitrary number of subsystems is additive over the constituent subsystems. This is the additivity property of entropy.