Tsallis’ ‘statistical thermodynamic’ formulation of the nonadditive entropy of degree-α is neither correct nor self-consistent. It is well known that the maximum entropy formalism [1], the minimum discrimination information [2], and Gauss’ principle [3, 4] all lead to the same results when a certain condition on the prior probability distribution is imposed [5]. All these methods lead to the sa...

The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that Shannon entropy can be approximated by Rényi entropy or Tsallis entropy, which are both functions of the αth frequency moments and approach Shannon entropy a...

In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or Rényi statistics for nonextensive systems at equilibrium; 2) equilibrium N-body systems with nonad-ditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic equilibrium. The nonextensive statistics may be Tsallis or...

An computer-aided diagnosis system of pathological brain detection (PBD) is important for help physicians interpret and analyze medical images. We proposed a novel automatic PBD to distinguish pathological brains from healthy brains in magnetic resonance imaging scanning in this paper. The proposed method simplified the PBD problem to a binary classification task. We extracted the wavelet packe...

By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.

We introduce fractal Tsallis entropy and show that it satisfies Shannon–Khinchin axioms. Analogously to divergence (or relative entropy, according some authors), is defined properties of are studied. Within this framework, Lesche stability verified an example concerning the microcanonical ensemble given. generalize LMC complexity measure (LMC Lopez-Ruiz, Mancini Calbert), apply a two-level syst...