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Combinatorial basis and non-asymptotic form of the Tsallis entropy function. (English) Zbl 1189.82008

Summary: Using a \(q\)-analog of Boltzmann’s combinatorial basis of entropy, the non-asymptotic non-degenerate and degenerate combinatorial forms of the Tsallis entropy function are derived. The new measures - supersets of the Tsallis entropy and the non-asymptotic variant of the Shannon entropy - are functions of the probability and degeneracy of each state, the Tsallis parameter \(q\) and the number of entities \(N\). The analysis extends the Tsallis entropy concept to systems of small numbers of entities, with implications for the permissible range of \(q\) and the role of degeneracy.

MSC:

82B03 Foundations of equilibrium statistical mechanics
94A17 Measures of information, entropy

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