Symbolic sequences and Tsallis entropy

Abstract

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated l times, with the probability distribution p(l) ∝ 1/l µ . For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, for a suitable choice of q, a linear behavior. We also study the chain as a random walk-like process and observe a nonusual diffusive behavior depending on the values of the parameter µ.

Solutions for a q-generalized Schrödinger equation of entangled interacting particles

“…and the numerical solutions for ψ(x 1 , x 2 , t) are shown in Fig. (7). due to the interaction with the potential, the binding behavior appears in different times, see for example t = 50.…”

“…where k is a constant and q is a real parameter, has shown to be useful in the description of several systems where the additivity fails such as systems characterized by non-Markovian processes [3,4,6,7], nonergodic dynamics and long-range many-body interactions [5]. The nonadditive characteristic of S q [8,9,10] has also brought new insights to several works in the area of complex systems [9,10] and contributed to diverse problems of quantum mechanics [11,12,13,14,15,16,17,18,19,20,21].…”

Derivation of an amplitude of information in the setting of a new family of fractional entropies

“…These entropies depend upon a real-valued parameter a which has different meanings depending upon the considered phenomenon under investigation, and very often it is more or less related to fractal dimension. Shannon's entropy has been useful in coding theory [9] and all these entropies have been successfully applied to many fields [10,40,45,52,54], mainly via Jaynes' maximum entropy principle [13,14], like in synergetics (organization and self-organization), see for instance [11]. The reference [24] by Kapur displays a large sample of systems which are analyzed by using the maximum entropy principle.…”

Generating Pseudo-Random Discrete Probability Distributions

“…As a consequence, it is also an essential aspect of our science and technology. The related research theme, that was motivated initially mainly by gambling and led eventually to probability theory [4,5], is nowadays a crucial part of many different fields of study such as computational simulations, information theory, cryptography, statistical estimation, system identification, and many others [6,7,8,9,10,11,12].…”