Thermodynamics and statistical thermodynamics

In this course, we are going to develop some machinery for interrelating the statistical properties of a system containing a very large number of particles, via a statistical treatment of the laws of atomic or molecular motion. It turns out that once we have developed this machinery, we can obtain some very general results which do not depend on the exact details of the statistical treatment. These results can be described without reference to the underlying statistical nature of the system, but their validity depends ultimately on statistical arguments. They take the form of general statements regarding heat and work, and are usually referred to as classical thermodynamics, or just thermodynamics, for short. Historically, classical thermodynamics was the first sort of thermodynamics to be discovered. In fact, for many years the laws of classical thermodynamics seemed rather mysterious, because their statistical justification had yet to be discovered. The strength of classical thermodynamics is its great generality, which comes about because it does not depend on any detailed assumptions about the statistical properties of the system under investigation. This generality is also the principle weakness of classical thermodynamics. Only a relatively few statements can be made on such general grounds, so many interesting properties of the system remain outside the scope of this theory.

If we go beyond classical thermodynamics, and start to investigate the statistical machinery which underpins it, then we get all of the results of classical thermodynamics, plus a large number of other results which enable the macroscopic parameters of the system to be calculated from a knowledge of its microscopic constituents. This approach is known as statistical thermodynamics, and is extremely powerful. The only drawback is that the further we delve inside the statistical machinery of thermodynamics, the harder it becomes to perform the necessary calculations.

Note that both classical and statistical thermodynamics are only valid for systems in equilibrium. If the system is not in equilibrium then the problem becomes considerably more difficult. In fact, the thermodynamics of non-equilibrium systems, which is generally called irreversible thermodynamics, is a graduate level subject.