Robert K. Niven
Published 2004-12-17, updated 2005-05-16Version 2
The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a "binary decision", exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems.
Comments: 18 pages; 6 figures; accepted for publication by Physics Letters A, 13/5/05
Cost of s-fold Decisions in Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics
Derivation of Bose-Einstein and Fermi-Dirac statistics from quantum mechanics: Gauge-theoretical structure
Bose-Einstein vs. electrodynamic condensates: the question of order and coherence
