We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes’ inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the nonnegative matrices in the framework of matrix ana...

I present empirical comparisons between a standard statistical translation model and an equivalent Maximum Entropy model. Results show that the Maximum Entropy model is promising, but highly sensitive to the method of feature selection.

True random number generators (TRNGs) are essential for cryptographic systems, and they are usually evaluated by the concept of entropy. In general, the entropy of a TRNG is estimated from its stochastic model, and reflected in the statistical results of the generated raw bits. Oscillator-based TRNGs are widely used in practical cryptographic systems due to its elegant structure, and its stocha...

It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular interpretation of Shannon’s H-function (related to consecutive measurements), and is shown explicitly to fail for other physical interpretations. Further, it is s...

We study b, c quark hadronization from QGP. We obtain the yields of charm and bottom flavored hadrons within the statistical hadronization model. The important novel feature of this study is that we take into account the high strangeness and entropy content of QGP, conserving strangeness and entropy yields at hadronization. PACS. 25.75.Nq Quark deconfinement – 12.38.Mh Quark-gluon plasma in qua...

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculati...

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to 'prove' the pri...

We review and further develop a mathematical framework for non-equilibrium quantum statistical mechanics recently proposed in [JP4, JP5, JP6, Ru3, Ru4, Ru5, Ru6]. In the algebraic formalism of quantum statistical mechanics we introduce notions of non-equilibrium steady states, entropy production and heat fluxes, and study their properties. Our basic paradigm is a model of a small (finite) quant...

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...

Tsallis and Rényi entropy measures are two possible different generalizations of the Boltzmann-Gibbs entropy (or Shannon’s information) but are not generalizations of each others. It is however the Sharma-Mittal measure, which was already defined in 1975 (B.D. Sharma, D.P. Mittal, J.Math.Sci 10, 28) and which received attention only recently as an application in statistical mechanics (T.D. Fran...