## Molecules Are Correlated! Multidimensional Statistical Mechanics

We can now extend our understanding of statistical mechanics to much more realistic systems. Most systems of interest, of course, are “macroscopic” and contain not just complicated molecules, but many, many copies of them. You can guess that mathematical complexity is about to set in. But don’t panic-all of the intuition we developed in one-dimensional systems remains highly pertinent. Free energy still “means” probability, and entropy still describes the size of a state. It’s true even in high-dimensional systems that we should expect an average energy of kBT/2 per degree of freedom. Part of this chapter will be devoted to showing you that one-dimensional reasoning still works.