Thermodynamics of Generalized Fermi Systems in a Harmonic Trap

Thermodynamics of the generalized ideal Fermi systems in the two-and three-dimensional harmonic traps are respectively calculated by the Tsallis entropy in this paper. The influences of the trap and q-number on the thermodynamic parameters (epically the heat capacity) are analysed in detail. The results yield a well agreement with the classical cases.

Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

Non-extensive statistical mechanics and the thermodynamic stability of FRW universe

In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of the universe are obtained. For the Tsallis entropy model, we obtained the constraint for β, namely, 1/2 <β <2. The free energy of a thermal equilibrium universe must be less than zero. We suggest that the reason for the accelerated expansion of the universe is not due to Tsallis entropy. Similar results are obtained for loop quantum gravity. However, since the values of Λ(γ) and q cannot be determined in this model, the results become more subtle than that in the Tsallis entropy model. In addition, we compare the results for the universe with those for a Schwarzschild black hole.

On Conditional Tsallis Entropy

There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter α that converges to the Shannon entropy as α approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature—their properties are studied and their values, as a function of α, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter α.

A bound on expectation values and variances of quantum observable via Rényi entropy and Tsallis entropy

Entropy is a key concept of quantum information theory. The entropy of a quantum system is a measure of its randomness and has many applications in quantum communication protocols, quantum coherence, and so on. In this paper, based on the Rényi entropy and Tsallis entropy, we derive the bounds of the expectation value and variance of quantum observable respectively. By the maximal value of Rényi entropy, we show an upper bound on the product of variance and entropy. Furthermore, we obtain the reverse uncertainty relation for the product and sum of the variances for [Formula: see text] observables respectively.

Tsallis Entropy of Uncertain Random Variables and Its Application

Tsallis entropy ia a flexible extension of Shanon (logarithm) entropy. Since, entropy measures indeterminacy of an uncertain random variable, this paper proposes the concept of partial Tsallis entropy for uncertain random variables as a flexible devise in chance theory. An approach for calculating partial Tsallis entropy for uncertain random variables, based on Monte-Carlo simulation, is provided. As an application in finance, partial Tsallis entropy is invoked to optimize portfolio selection of uncertain random returns via crow search algorithm.

Analysis of Time Series Based on a New Entropy Plane by Using Weighted Dispersion Pattern

Complexity is an important feature of complex time series. In this paper, we construct a weighted dispersion pattern and propose a new entropy plane using past Tsallis entropy and past Rényi entropy by using weighted dispersion pattern (PTEWD and PREWD, respectively), to quantify the complexity of time series. Through analyzing simulated data and actual data, we have verified the reliability of the entropy plane method. This entropy plane successfully distinguishes American and Chinese stock indexes, as well as developed and emergent stock markets. We introduce PTEWD and PREWD into multiscale settings, which could also well distinguish different stock markets. The results show that the new entropy plane could be used as an effective tool to distinguish financial markets.

Alternative Dirichlet Priors for Estimating Entropy Via a Power Sum Functional

Entropy is a functional of probability and is a measurement of information contained in a system; however, the practical problem of estimating entropy in applied settings remains a challenging and relevant problem. The Dirichlet prior is a popular choice in the Bayesian framework for estimation of entropy when considering a multinomial likelihood. In this work, previously unconsidered Dirichlet type priors are introduced and studied. These priors include a class of Dirichlet generators as well as a noncentral Dirichlet construction, and in both cases includes the usual Dirichlet as a special case. These considerations allow for flexible behaviour and can account for negative and positive correlation. Resultant estimators for a particular functional, the power sum, under these priors and assuming squared error loss, are derived and represented in terms of the product moments of the posterior. This representation facilitates closed-form estimators for the Tsallis entropy, and thus expedite computations of this generalised Shannon form. Select cases of these proposed priors are considered to investigate the impact and effect on the estimation of Tsallis entropy subject to different parameter scenarios.