A non-linear, generalized Fokker-Planck (GFP) equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by Tsallis in his generalization of Statistical Mechanics. In the case of a constant or linearly varying drift, the time dependent solutions of the...

A method for finding the state distribution in a physical system, on the basis of a detailed analysis of the experimental response of the system to an external probe, is presented. The concomitant algorithm, based upon the maximum entropy principle, is specifically devised so as to take into...

Statistical Mechanics (SM) has been quite successful in providing one with exact, or at least approximate, descriptions of the time-dependent solutions of the Liouville (or of the von Neumann) equation within the context of Hamiltonian dynamics (HD). Here we investigate how to extend some of its...

Invariants of the Lewis kind are introduced within the context of Statistical Mechanics via information theory concepts. Several invariants of the Liouville equation are in this way built-up. Both the classical and the quantal cases are studied. Some applications are discussed. It is shown that...

In connection with Tsallis' generalized statistical mechanics, we discuss the associated quantal distribution functions and show, by recourse to elementary considerations, that nonextensivity entails apparent violations to the Pauli principle. The typical zero temperature sharp Fermi surface is...

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.

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.

Arguments of the Jaynes' maximum entropy sort have proved to be surprisingly successful in providing one with approximate descriptions of pure states in a variety of scenarios, entirely bypassing any consideration of Schrödinger's equation. Thus far, however, the concomitant algorithm was...

We investigate the changes in the entanglement of formation ΔE produced by quantum logical gates acting on composite quantum systems. We consider two-qubit, three-qubit, and two-qutrit systems. We prove that the ΔE-distributions generated by different quantum gates that can be obtained from...

Fisher's information measures, as adapted to a nonextensive (Tsallis) environment, are discussed. For systems of particles that are in a general state of motion a lower bound to these information measures is derived with the help of a recently established upper bound to the entropy increase....