Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those systems with powerlaw behaviour, where the use of the Tsallis entropy is relevant. We discuss a specific class of dynam...

We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that there is a distinguished dependence of the entropic index q on the spatial scale that makes the Tsallis entropies quasi-additive. Quasi-additivity implies th...

A maximum entropy framework based on Tsallis entropy is proposed to depict long tail behavior of queue lengths in broadband networks. Queue length expression as measured in terms of number of packets involves Hurwitz-zeta function. When the entropy parameter q in Tsallis entropy is less than unity, the distribution of packets yields power law behavior. In the limit q tending to unity, Tsallis e...

We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vest.Leningrad Gros.Univ. 7 (1962) 135) and Lynden-Bell & Wood (Mon.Not.R.Astron.Soc. 138 (1968) 49...

The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. Most of them, however, are greedy algorithms which have the drawback of obtaining only local optimums. Besides, common split criteria, e.g. Shannon entropy, Gain ...

We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis’ non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press (condmat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structur...

We present a first physical application of Tsallis’ generalized entropy to the thermodynamics of self-gravitating systems. The stellar system confined in a spherical cavity of radius re exhibits an instability, so-called gravothermal catastrophe, which has been originally investigated by Antonov (Vest.Leningrad Gros.Univ. 7 (1962) 135) and Lynden-Bell & Wood (Mon.Not.R.Astron.Soc. 138 (1968) 49...

1. Introduction This paper reviews recent work on the properties of Tsallis distributions, Tsallis statistics, anomalous diffusion and multi-fractal processes. Processes of this kind have the capacity to represent natural phenomena that are associated with turbulence and emerging complexity. However, in addition they may also capture crucial aspects of human decision-making in response to condi...