https://doi.org/10.1140/epjb/e2008-00038-8
Combinatorial basis and non-asymptotic form of the Tsallis entropy function
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 Ø, Denmark
3
Department of Information and Image Sciences, Faculty of Engineering, Chiba University, Chiba, 263-8522, Japan
Corresponding author: a r.niven@adfa.edu.au
Received:
5
October
2007
Revised:
11
December
2007
Published online:
31
January
2008
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.
PACS: 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008
