Related papers: On Tsallis nonequilibrium entropy evolution
We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the…
The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat and work to non-equilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate…
Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic…
In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space…
Probability distributions defined on the half space are known to be quite different from those in the full space. Here, a nonextensive entropic treatment is presented for the half space in an analytic and self-consistent way. In this…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This…
Within a framework of utmost generality, we show that the entropy maximization procedure with linear constraints uniquely leads to the Shannon-Boltzmann-Gibbs entropy. Therefore, the use of this procedure with linear constraints should not…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
We present an embedding of the Tsallis entropy into the 3-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy…
This paper addresses the problem of dynamic asset allocation under uncertainty, which can be formulated as a linear quadratic (LQ) control problem with multiplicative noise. To handle exploration exploitation trade offs and induce sparse…
In this paper we discuss the meaning of the Schnakenberg formula for entropy production in non-equilibrium systems. To this end we consider a non-equilibrium system as part of a larger isolated system which includes the environment. We…
The relation between the thermodynamic entropy production and non-Markovian evolutions is matter of current research. Here, we study the behavior of the stochastic entropy production in open quantum systems undergoing unital non-Markovian…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
We study non-equilibrium quantum dynamics of the single-component scalar field theory in 1+1 space-time dimensions on the basis of the Kadanoff-Baym equation including the next-to-leading-order (NLO) skeleton diagrams. As an extension of…
In this paper, we investigate new procedures for statistical testing based on Tsallis entropy, a parametric generalization of Shannon entropy. Focusing on multivariate generalized Gaussian and $q$-Gaussian distributions, we develop…
We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young inequalities are also given. In addition, operator inequalities for normalized positive linear…
A nonextensive thermostatic approach to chaotic dynamical systems is developed by expressing generalized Tsallis distribution as escort distribution. We explicitly show the thermodynamic limit and also derive the Legendre Transform…
We provide evidence that the small-scale statistics of the acceleration of a test particle in high-Reynolds number Lagrangian turbulence is correctly described by Tsallis statistics with entropic index q=3/2. We present theoretical…
A generalization of the entropy production rate is proposed $\Pi_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the R\'enyi entropy $S_q$ ,…