Related papers: Vanishing largest Lyapunov exponent and Tsallis en…
In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a nonadditive generalization of Shannon entropy. We obtain several results of…
In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for…
The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis…
In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the…
The Lagrangian technique of Niven (2004, Physica A, 334(3-4): 444) is used to determine the constrained forms of the Tsallis entropy function - i.e. Lagrangian functions in which the probabilities of each state are independent - for each…
We study the hyperbolicity of a class of horseshoes exhibiting an internal tangency, i.e. a point of homoclinic tangency accumulated by periodic points. In particular these systems are strictly not uniformly hyperbolic. However we show that…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed…
One dimensional intermittent maps with stretched exponential separation of nearby trajectories are considered. When time goes infinity the standard Lyapunov exponent is zero. We investigate the distribution of $\lambda_{\alpha}=…
Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] recently stated that the Tsallis entropy violates the third law of thermodynamics for $0 < q <1$ in the sub-additive regime. We first show that the division between the regimes $q < 1$…
We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows…
We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index $\alpha>1$ describes 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…
In high-energy collisions the number of the created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy…
We analytically investigate the thermodynamic variables of a hot and dense system, in the framework of the Tsallis non-extensive classical statistics. After a brief review, we start by recalling the corresponding massless limits for all the…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
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,…