The Physical Basis of the Gibbs-von Neumann entropy
Abstract
Description
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a consequence of Hamiltonian dynamics. The mathematical treatment utilises well known results [Gib02, Tol38, Weh78, Par89], but most importantly, incorporates a variety of arguments on the phenomenological properties of thermal states [Szi25, TQ63, HK65, GB91] and of statistical distributions[HG76, PW78, Len78]. This enables the identification of the canonical distribution as the unique representation of thermal states without approximation or presupposing the existence of an entropy function. The Gibbs-von Neumann entropy is then derived, from arguments based solely on the addition of probabilities to Hamiltonian dynamics.
42 pages, no figures (3rd version substantial revision and simplification of central argument incorporating adiabatic availability and passive distributions)
42 pages, no figures (3rd version substantial revision and simplification of central argument incorporating adiabatic availability and passive distributions)