Combinatorial basis and non-asymptotic form of the Tsallis entropy function |
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Authors: | R. Niven H. Suyari |
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Affiliation: | 1. School of Aerospace, Civil and Mechanical Engineering, The University of New South Wales at ADFA, Northcott Drive, Canberra, ACT, 2600, Australia 2. Niels Bohr Institute, University of Copenhagen, Copenhagen ?, Denmark 3. Department of Information and Image Sciences, Faculty of Engineering, Chiba University, Chiba, 263-8522, Japan
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Abstract: | 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. |
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Keywords: | 02.30.-f Function theory, analysis 02.50.Cw Probability theory 05.20.-y Classical statistical mechanics 05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems |
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