The Meaning of Temperature and Entropy in Classical Statistical Mechanics

This paper began life as a serious attempt to understand the classical foundations of thermodynamics, but ended up doing crazy things like defining the temperature and entropy of single molecules. Nevertheless, there is method behind the madness, because in terms of these generalized definitions I am able to prove that the generalized notion of temperature reduces to the standard notion under certain quite general conditions, in which case the standard entropy is equal to the sum of the molecular entropies. The generalized viewpoint is intended to provide a deeper understanding of how statistical mechanics works, ...and why it doesn’t work, sometimes, as in the case of a single particle in a box. The purpose of such examples is to make a conceptual point, not to advance physics.