Introduction

This chapter discusses physical systems involving large number of particles, conventionally called statistical mechanics. Because these concepts are used in several later chapters, a complete and pedagogical discussion is presented here. We begin with the equilibrium statistical mechanics of classical systems and derive macroscopic thermodynamics from statistical mechanics. In the second half of the chapter we deal with quantum statistical mechanics, including the physics of Fermi gas. This chapter depends on the concepts developed in the previous three chapters and will be needed for Chaps. 6 (radiative processes), 8 (neutral fluids), 9 (plasma physics) as well as in the study of stellar evolution and stellar remnants (Vol. II) and the thermal history of the universe (Vol. III).

Operational Basis of Statistical Mechanics

The dynamical evolution of any system can be studied most conveniently by use of the concept of phase space developed in Chap. 2, Section 2.2. For a system of N-point particles the phase space will be 6N dimensional. Given the initial state of the system as a point in the phase space, the dynamical evolution of the system traces out a one-dimensional curve in the 6N-dimensional phase space, starting from the given point. If the equations of motion for the system are solved exactly (with the given initial conditions), then this curve in the phase space can be determined exactly.

For any realistic N-particle system, this task is impossible even with the best computers available today.