Escort–Husimi distributions, Fisher information and nonextensivity

On escort distributions, q-gaussians and Fisher information

Escort distributions are a simple one parameter deformation of an original distribution p. In Tsallis extended thermostatistics, the escort-averages, defined with respect to an escort distribution, have revealed useful in order to obtain analytical results and variational equations, with in particular the equilibrium distributions obtained as maxima of Rényi-Tsallis entropy subject to constrain...

A Sequence of Escort Distributions and Generalizations of Expectations on q-Exponential Family

Academic Editors: Frédéric Barbaresco and Frank Nielsen Received: 26 October 2016; Accepted: 19 December 2016; Published: 25 December 2016 Abstract: In the theory of complex systems, long tailed probability distributions are often discussed. For such a probability distribution, a deformed expectation with respect to an escort distribution is more useful than the standard expectation. In this pa...

Fisher Information and Semiclassical Treatments

We review here the difference between quantum statistical treatments and semiclassical ones, using as the main concomitant tool a semiclassical, shift-invariant Fisher information measure built up with Husimi distributions. Its semiclassical character notwithstanding, this measure also contains abundant information of a purely quantal nature. Such a tool allows us to refine the celebrated Lieb ...

A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it de nes a parametric curve that we call an escort-path. The Rényi divergence appears as a natural by-product of the setting. We study the dynamics of the Fisher information on this path, and show in particular that the t...

Husimi Distribution and the Fisher Information