2007/01/17 by O. J. E. Maroney, Maroney, O. J. E. · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0701127
42 pages, no figures (3rd version substantial revision and simplification of central argument incorporating adiabatic availability and passive distributions)
openalex publication_date 2007/01/17 · arxiv created 2008/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.