Related papers: Information Shift Dynamics Described by Tsallis $q…
The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for…
We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
We study the strong Borel-Cantelli property both for events and for shifts on sequence spaces considering both a conventional and a nonconventional setups. Namely, under certain conditions on events $\Gamma_1,\Gamma_2,...$ we show that with…
The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
We study 1-dimensional coupled map lattices consisting of diffusively coupled Tchebyscheff maps of N-th order. For small coupling constants a we determine the invariant 1-point and 2-point densities of these nonhyperbolic systems in a…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal…
It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…
We study the evolution of Tsallis entropy along the heat flow and establish its concavity in arbitrary dimensions. Extending prior results that were restricted to the one-dimensional setting, we prove that the Tsallis entropy is concave in…
We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified…
This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the…
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…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…