Basics of Equilibrium Statistical Mechanics
The basics of equilibrium statistical mechanics are developed. We first derive a statistical-mechanical expression for entropy, (2.10) called the Gibbs or von Neumann entropy, that is compatible with the laws of thermodynamics. It is used subsequently to find the equilibrium statistical distributions, namely, microcanonical, canonical, and grand canonical distributions as (2.12), (2.18), and (2.26), respectively, based on the principle of maximum entropy by Jaynes.
KeywordsPartition Function Lagrange Multiplier Maximum Entropy Helmholtz Free Energy Grand Canonical Ensemble
- 1.J.W. Gibbs, Elementary Principles in Statistical Mechanics (Yale University Press, New Haven, 1902), pp. 44–45 and 168Google Scholar
- 3.L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd edn. (Butterworth-Heinemann, Oxford, 1991)Google Scholar
- 4.O. Penrose, Foundations of Statistical Mechanics (Pergamon, Oxford, 1970). The footnote of p. 213Google Scholar
- 5.J.J. Sakurai, Modern Quantum Mechanics, rev. edn. (Addison-Wesley, New York, 1994)Google Scholar