Cost of s-fold decisions in exact Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics
✍ Scribed by Robert K. Niven
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 469 KB
- Volume
- 365
- Category
- Article
- ISSN
- 0378-4371
No coin nor oath required. For personal study only.
✦ Synopsis
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).