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- W1628117987 abstract "The rigorous version of the result that unifies Maxwell-Boltzmann, Bose-Einstein statistics and Zipf-Mandelbrot Law is presented in the paper. Additionally, the Fluctuation theorem is included. Both results are set in the rigorous probabilistic framework. The system under consideration is composed of fixed number of particles and energy smaller than some prescribed value. The particles are redistributed on fixed number of energy levels and are indistinguishable within one level. Further, the degenerations of energy levels are included and their number increases as the number of particles increase. The three distribution mentioned in the title corresponds to the three asymptotic cases of rate of increases of degenerations as a function of particles. When we take a thermodynamic limit for three cases we basically obtain the Law of Large Numbers and the obtained three means are our distributions. The fluctuations, i.e. the deviation from the mean turns out depends on the Entropy of the system. When its maximum is in inside of the domain we get Gaussian distribution. When it is on the boundary we get discrete distribution in the direction orthogonal to the boundary on which maximum is situated and Gaussian in other directions. The proof is similar for both results. The main part are the properties and asymptotic behavior of Entropy. Due to this we can optimize it and therefore apply probabilistic results which underlying assumptions overlap with ours and eventually get the desired results." @default.
- W1628117987 created "2016-06-24" @default.
- W1628117987 creator A5043695009 @default.
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- W1628117987 date "2015-01-27" @default.
- W1628117987 modified "2023-09-27" @default.
- W1628117987 title "Unification of Maxwell-Boltzmann, Bose-Einstein statistics and Zipf-Mandelbort Law with Law of Large Numbers and corresponding Fluctuation theorem" @default.
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