This work analyzes the classical statistical mechanics associated to phase-space curves in three dimensions. Special attention is paid to the entropic force. Strange effects like confinement, hard core, and asymptotic freedom are uncovered.

We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 307 (2008)]. By recourse to tempered ultradistributions we show that this complex-plane generalization overcomes all the troubles that afflict its...

We introduce here the q-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q-Gaussian instance receives special consideration. Also, we derive the q-partition function from the q-Laplace transform.

In this work, we generalize previous results about the Fractionary Schrödinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green function for a free particle in the general case,...

The study of conditional q-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The q-entropies depend on the density matrix <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\rho$</EquationSource> </InlineEquation> through the quantity <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$\omega_q={\rm Tr}\rho^q$</EquationSource> </InlineEquation>, and admit...</equationsource></inlineequation></equationsource></inlineequation>

Our protagonists are (i) the Cressie–Read family of divergences (characterized by the parameter γ), (ii) Tsallis’ generalized relative entropies (characterized by the q one), and, as a particular instance of both, (iii) the Kullback–Leibler (KL) relative entropy. In their normalized...

We generate a family of phase space, thermal coherent-state’s representations, within the framework of Tsallis’ Generalized Statistical Mechanics and study their properties. Our protagonists are q-gaussian distributions. We obtain analytical expressions for the most important...

Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the...

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q1, they can be constructed as conditional distributions of...

Information concerning important details of an ecosystem's evolution are shown to be contained in an appropriately constructed power spectrum. In particular, it provides an answer to the question of just why power-law behavior vanishes in the absence of Darwinian competition.