Related papers: The unique, universal entropy for complex systems
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
We extend the Hanel and Thurner asymptotic analysis to both extensive and non-extensive entropies on the basis of a wide class of entropic forms. The procedure is known to be capable to classify multiple entropy measures in terms of their…
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…
To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series of such entropies have been proposed in…
We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…
The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the…
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…
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…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…