Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-07-24
Physica A375 (2007) 110-122
Physics
Condensed Matter
Statistical Mechanics
LaTeX, 22 pages
Scientific paper
10.1016/j.physa.2006.09.002
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Renyi, Tsallis, and Havrda-Charvat entropies. The generalized entropy measure introduced here is also shown to haveinteresting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics (Tsallis, 1988) and superstatistics introduced by Beck and Cohen (2003). The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.
Haubold Hans Joachim
Mathai Arak Mathai
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