Microstate probabilities

In Chapter 3 we discussed the way the world works at a microscopic level: the interactions and laws governing the time evolution of atoms and molecules. We found that an important, unifying perspective for both quantum and classical descriptions is the concept of energy. Now we take a macroscopic point of view. What happens when many (~1023) molecules come together, when we cannot hope to measure individual atomic properties but can probe only bulk material ones? As the title of this chapter suggests, the relevant concept at the macro-resolution is entropy.

Remember that from a macroscopic perspective, we care about macrostates, that is, states of a system characterized by a few macroscopic variables, like E, V, N, T, or P. Empirical measurements generally establish values for properties that are the net result of many atomic interactions averaged over time, and we are thus able to describe a system only in terms of these large-scale, reduced-information metrics that smooth over the molecular world. The statement that a system is at one specific macrostate actually implies that it is evolving through a particular ensemble of many microscopic configurations.

We will focus on classical isolated systems because these offer the simplest introductory perspective. Let us imagine that a closed, insulated container of molecules evolves in time.