5 research outputs found
H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
In the present effort we consider the most general non linear particle
kinetics within the framework of the Fokker-Planck picture. We show that the
kinetics imposes the form of the generalized entropy and subsequently we
demonstrate the H-theorem. The particle statistical distribution is obtained,
both as stationary solution of the non linear evolution equation and as the
state which maximizes the generalized entropy. The present approach allows to
treat the statistical distributions already known in the literature in a
unifying scheme. As a working example we consider the kinetics, constructed by
using the -exponential recently proposed which reduces to
the standard exponential as the deformation parameter approaches to
zero and presents the relevant power law asymptotic behaviour
. The -kinetics obeys the H-theorem and in the case of
Brownian particles, admits as stationary state the distribution
which can be obtained also
by maximizing the entropy with after properly constrained.Comment: To appear in Phys. Lett.
Wootters' distance revisited: a new distinguishability criterium
The notion of distinguishability between quantum states has shown to be
fundamental in the frame of quantum information theory. In this paper we
present a new distinguishability criterium by using a information theoretic
quantity: the Jensen-Shannon divergence (JSD). This quantity has several
interesting properties, both from a conceptual and a formal point of view.
Previous to define this distinguishability criterium, we review some of the
most frequently used distances defined over quantum mechanics' Hilbert space.
In this point our main claim is that the JSD can be taken as a unifying
distance between quantum states.Comment: 15 pages, 3 figures, changed content, added reference for last
sectio
A Schroedinger link between non-equilibrium thermodynamics and Fisher information
It is known that equilibrium thermodynamics can be deduced from a constrained
Fisher information extemizing process. We show here that, more generally, both
non-equilibrium and equilibrium thermodynamics can be obtained from such a
Fisher treatment. Equilibrium thermodynamics corresponds to the ground state
solution, and non-equilibrium thermodynamics corresponds to excited state
solutions, of a Schroedinger wave equation (SWE). That equation appears as an
output of the constrained variational process that extremizes Fisher
information. Both equilibrium- and non-equilibrium situations can thereby be
tackled by one formalism that clearly exhibits the fact that thermodynamics and
quantum mechanics can both be expressed in terms of a formal SWE, out of a
common informational basis.Comment: 12 pages, no figure