The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffu...

In this paper the notion of robust entropy and subsequently, robust entropy rate for a family of discrete time uncertain sources is introduced. When the uncertainty is described by a relative entropy constraint between the set of uncertain source densities and a given nominal source density, the solution to this robust notion of information is presented and its connection with other notions of ...

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This en-tropy is a variant of the generalized entropy of order α, considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Rényi, Tsallis, and Havrda-Charvát entropies. The generalized entropy measure introduced here is also shown to...

This study makes use of the Tsallis entropy to predict the shear stress distribution. Given a definition of the Tsallis entropy, it is maximized by using the probability density function, which then is used to attain a novel shear stress equation. This is then employed for calculating the shear stress distribution in rectangular channels in different aspect ratios and finally, for viability, th...

Relative entropy of coherence can be written as an difference the original state and incoherent closest to it when measured by relative entropy. The natural question is, if we generalize this situation Tsallis or Rényi entropies, would define good measures? In other words, a between entropies Taking instead entropy, leads well-known distance-based coherence, which means expression defined measu...

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated l times, with the probability distribution p(l) ∝ 1/lμ. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, f...

1. The Physics of Information 2 2. Thermodynamics 2 2.1. The laws 3 2.2. Free energy 6 3. Statistical mechanics 7 3.1. Definitions and postulates 8 3.2. A simple model system of magnetic spins 9 3.3. The Maxwell-Boltzmann distribution 10 3.4. Free energy revisited 11 3.5. Gibbs entropy 12 4. Nonlinear dynamics 12 4.1. The ergodic hypothesis 13 4.2. Chaos and limits to prediction 14 4.3. Quantif...

We provide a unifying axiomatics for Rényi’s entropy and non–extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszár’s measure of directed divergence known from communication theory.

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...