Probability Distributions in Statistical Physics

Mark Kon

Ahmad Abu Taleb

Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles where any of them can be a fermion with probability [P] and can be a boson with probability [1-P]?. In this paper this question is solved

Barry Loewer

Temur Z. Kalanov

Abstract. Modern analysis of the Boltzmann distribution on the basis of probability theory and of Gibbs quantum canonical distribution is proposed. It is shown that the Boltzmann distribution function is neither a reliable result of probability theory nor a consequence of Gibbs quantum canonical distribution. Conclusion is that the Boltzmann distribution function has no statistical and physical meaning, and the concept “Boltzmann distribution” should be abolished.

G. Boffetta, Angelo Vulpiani

Bernard H. Lavenda, Jeremy Dunning-Davies

It is shown that intermediate statistics do not correspond to any physical process. The stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi–Dirac and Bose–Einstein statistics. The binomial and negative binomial distributions, characterizing Fermi–Dirac and Bose–Einstein statistics, respectively, transform into the Poisson distribution, descriptive of classical statistics, as the number of energy cells increases without limit. These distributions are shown to be the laws of error leading to the average value as the most probable value.