Starting with a classical Hamiltonian function H, we show that, if we select among its phase–space trajectories those that minimize Fisher’s information measure, the resulting trajectories coincide with the stationary ones of their quantum counterparts. Hˆ of H.

We devise a maximum entropy technique to construct (approximate) time-dependent solutions to evolution equations endowed with source terms and, consequently, not preserving normalization. In some special cases the method yields exact solutions. It is shown that the present implementation of the...

Consider a bipartite quantum system with at least one of its two components being itself a composite system. By tracing over part of one (or both) of these two subsystems it is possible to obtain a reduced (separable) state that exhibits quantum correlations even if the original state of the...

Via a first-order linear differential equation, we determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon’s or Tsallis’ entropies in the concomitant variational problem. It is shown that the two...

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 discuss some interesting peculiarities of Tsallis' quantum thermostatistics in relation with dynamical evolution, with particular emphasison the cut-off condition question. The existence of special dynamical states that do not appear in the Boltzmann-Gibbs thermostatics is analyzed in detail.