# A Probabilistic Foundation of Statistical Mechanics

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## Abstract

Reviewing a book on statistical mechanics, Percus notes that “Equilibrium statistical mechanics —as a branch of physics— is a strange discipline. It must logically be a consequence of mechanics, but the fashion in which this holds is far from settled”.

^{1}Perhaps by advancing this consideration, this author would affirm that what is far from settled is the extent to which thermodynamical laws are consequences of mechanical ones. Or, on the contrary, how much of statistical mechanics is bounded to probability laws and how much not. In fact, the usual way to build up this discipline is based on a mixture of undeterministic (probability) and deterministic (non-probability) principles. One example of a probability principle is that of equal weight:in a thermal equilibrium state of isolated system, each of the microscopic states belonging to the set

M(E, δE) is realized with equal probability.^{2}

## Keywords

Statistical Mechanic Probability Function Occupation Number Identical Particle Inductive Logic
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## Notes

- 1.J. K. Percus,
*Foundations of Physics*21 (1991) 257–8.CrossRefGoogle Scholar - 2.R. Kubo,
*Statistical Mechanics*, North-Holland Amsterdam 1990, p. 516.Google Scholar - 3.Ibid. p. 9.Google Scholar
- 4.D. Costantini and U. Garibaldi, “Classical and Quantum Statistics as Finite Random Processes”,
*Foundations of Physics*19 (1989) 743–754.CrossRefGoogle Scholar - 5.D. Costantini and U. Garibaldi, “Microcanonical and Canonical Distribution and Finite Exchangeable Random Processes”, to appear in
*Foundations of Physics*.Google Scholar - 6.This part deals with grandcanonical distributions.Google Scholar
- 7.R. Carnap, “A Basic System of Inductive Logic. Part P”,
*Studies in Inductive Logic and Probability*, (Carnap and Jeffrey eds) University of California Press Berkeley 1971, 33–165.Google Scholar - 8.D. Costantini and U Garibaldi, “Classical and Quantum Statistics as Finite Random Processes”, op. cit.Google Scholar
- 9.E. T. Jaynes,
*Paper on Probability, Statistics, and Statistical Physics*(Rosenkrantz ed), Reidel P. C. Dordrecht 1983.Google Scholar - 10.J. Tersoff and D. Bayer, “Quantum Statistics for Distinguishable Particles”
*Physical Review Letters*50 (1983) 553.CrossRefGoogle Scholar - 11.L. Brillouin, “Comparison des differents statistiques appliquee aux problemes de Quanta”,
*Annales de Phisigue*VII (1927) 315–331.Google Scholar

## Copyright information

© Springer Science+Business Media Dordrecht 1994