ABSTRACT
This chapter begins with the statistical mechanics, the modeling and prediction of the properties of materials from the structures of the atoms and molecules of which they are composed. The core of statistical mechanics is modeling the probability distributions of the energies of atoms and molecules. The various averages over those distributions are what experiments measure. For example, to compute the properties of gases, one needs the distributions of their energies and velocities. The central result in the chapter is the Boltzmann distribution law, which gives probability distributions from the underlying energy levels. The system is one four-bead chain that has two energy levels. Each energy level represents the number of bead–bead contacts that the chain can make. Conformations with the maximum number of bead–bead contacts have zero energy. Sometimes, there are intrinsically a different number of ways that a system can occupy one energy level than another. For example, for the four-bead polymer, each configuration is one microstate.
