In this chapter we will describe how statistical mechanics can be applied to obtain some important results in astrophysics. As an application of classical statistical mechanics we will discuss the Saha ionization formula which plays a role in determining the surface temperature of a star and which will be shown to follow from an analysis of chemical reactions involving ionized particles using statistical mechanics.

We have already emphasized in the last chapter that quantum mechanics has profound implications for the equations of state and, in particular, the stability of matter. In this chapter we will illustrate this effect by considering the collapse of stellar objects. A prominent example is that of white dwarf stars which are stabilized by the Pauli exclusion principle. Understanding white dwarf stars will involve Fermi-Dirac statistics. We will also briefly discuss the fact that neutron stars contain more neutrons than protons and will show that this follows from the analysis of a particular nuclear reaction process treated as a chemical reaction.

In order to present these examples in a suitable setting we start by reviewing a few basic facts about the physics of stellar evolution and we outline the principles that are used to model these objects. This is followed by a qualitative account of stellar evolution. With this background in place the specific examples are considered. We then close this chapter with a qualitative discussion of the cosmic background radiation.