The Physical Basis of the Gibbs-von Neumann entropy

Details The Physical Basis of the Gibbs-von Neumann entropy The Physical Basis of the Gibbs-von Neumann entropy

2007-01-17

arxiv.org/abs/quant-ph/0701127v2

Physics

Quantum Physics

42 pages, no figures (3rd version substantial revision and simplification of central argument incorporating adiabatic availabi

Scientific paper

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.

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