Cost of s-fold decisions in exact Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics

Robert K. Niven

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 142-149

Abstract: The exact forms of the degenerate Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation [R.K. Niven, Physics Letters A, 342(4) (2005) 286], are further examined. Firstly, an apparent paradox in quantization effects is resolved using the Laplace–Jaynes interpretation of probability. The energy cost of learning that a system, distributed over s equiprobable states, is in one such state (an “s-fold decision”) is then calculated for each statistic. The analysis confirms that the cost depends on one's knowledge of the number of entities N and (for BE and FD statistics) the degeneracy, extending the findings of Niven (2005).

Keywords: Entropy; Information theory; Combinatorial; Statistical mechanics; Measurement problem; Maxwell's demon (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:142-149

DOI: 10.1016/j.physa.2006.01.021

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