Related papers: Example of a possible interpretation of Tsallis en…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
The Tsallis distribution has been used widely in high energy physics to describe the transverse momnetum distributions of particles. In this note we show that the use of a thermodynamically consistent form of this distribution leads to a…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second…
We consider a simplified version of a solvable model by Mandal and Jarzynski, which constructively demonstrates the interplay between work extraction and the increase of the Shannon entropy of an information reservoir which is in contact…
We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present converse of Ando's inequality, for each parameter. We give examples to compare our results with the known…
Shannon entropy regularization is widely adopted in optimal control due to its ability to promote exploration and enhance robustness, e.g., maximum entropy reinforcement learning known as Soft Actor-Critic. In this paper, Tsallis entropy,…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
The exact solution of a particular form of the stationary state generalized Fokker-Planck equations, which is given under certain conditions by the classical Tsallis distribution, is compared with the solution of the MAXENT equations…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the…
Tsallis has proposed a generalisation of the standard entropy, which has since been applied to a variety of physical systems. In the canonical ensemble approach that is mostly used, average energy is given by an unnromalised, or normalised,…
We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…
A class of estimators of the R\'{e}nyi and Tsallis entropies of an unknown distribution $f$ in $\mathbb{R}^m$ is presented. These estimators are based on the $k$th nearest-neighbor distances computed from a sample of $N$ i.i.d. vectors with…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument…
I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…
We present a simple and general argument showing that a class of dynamical correlations give rise to the so-called Tsallis nonextensive statistics. An example of a system having such a dynamics is given, exhibiting a non-Boltzmann energy…