11. Basic and Quantum Thermodynamics

Chapter 6 mentioned the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein energy distributions of systems of weakly interacting particles. This chapter explains these results and then goes on to put quantum mechanics and thermodynamics in context.

It is assumed that you have had a course in basic thermodynamics. If not, rejoice, you are going to get one now. The exposition depends relatively strongly upon the material in chapter 5.7-5.9 and chapter 6.1-6.16.

This chapter will be restricted to systems of particles that are all the same. Such a system is called a “pure substance.” Water would be a pure substance, but air not really; air is mostly nitrogen, but the 20% oxygen can probably not be ignored. That would be particularly important under cryogenic conditions in which the oxygen condenses out first.

The primary quantum system to be studied in detail will be a macroscopic number of weakly interacting particles, especially particles in a box. Nontrivial interactions between even a few particles are very hard to account for correctly, and for a macroscopic system, that becomes much more so: just a millimol has well over 10$\POW9,{20}$ particles. By ignoring particle interactions, the system can be described in terms of single-particle energy eigenstates, allowing some real analysis to be done.

However, a system of strictly noninteracting unperturbed particles would be stuck into the initial energy eigenstate, or the initial combination of such states, according to the Schrö­din­ger equation. To get such a system to settle down into a physically realistic configuration, it is necessary to include the effects of the unavoidable real life perturbations, (molecular motion of the containing box, ambient electromagnetic field, cosmic rays, whatever.) The effects of such small random perturbations will be accounted for using reasonable assumptions. In particular, it will be assumed that they tend to randomly stir up things a bit over time, taking the system out of any physically unlikely state it may be stuck in and making it settle down into the macroscopically stable one, called “thermal equilibrium.”