Related papers: MAXENT and the Tsallis Parameter
Maxwell's first derivation of the equilibrium distribution function for a dilute gas is generalized in the spirit of the nonextensive q-statistics proposed by Tsallis. As an application, the q-Doppler broadening of spectral lines due to the…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
We studied multiple quantum harmonic oscillators in the Tsallis statistics of entropic parameter $q$ in the cases that the distributions are power-like, separately applying the conventional expectation value, the unnormalized…
We investigate first-order approximations to both i) Tsallis' entropy $S_q$ and ii) the $S_q$-MaxEnt solution (called q-exponential functions $e_q$). It is shown that the functions arising from the procedure ii) are the MaxEnt solutions to…
We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which…
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…
The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss simple physical applications of a system in the contact with finite heat bath or with temperature fluctuations. With help of the…
We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and Tsallis entropies. Related…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…
The necessary conditions (NC) that reconcile canonical probability distributions obtained from the q-maximum entropy principle, subjected to both i) the additive duality of generalized statistics and ii) normal averages expectations with…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
This paper brings together four distinct but very important physical notions: 1) Entropic force, 2) Entropy-along-a-curve, 3) Tsallis' q-statistics, and 4) Emergent gravitation. We investigate the non additive, classical (Tsallis')…
A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
By using the maximum entropy principle, with Tsallis entropy, we obtain an explicit dependence for energy distribution of earthquakes. This function describes very well the observations in a wide range of energies, where other distribution…
This expository note describes how to apply the method of maximum likelihood to estimate the parameters of the ``$q$-exponential'' distributions introduced by Tsallis and collaborators. It also describes the relationship of these…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…