623 research outputs found
A Shannon-Tsallis transformation
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 variations lead to equivalent solutions that take different appearances
but contain the same information. These solutions are linked by our
transformation
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
The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions
In this work, we generalize previous results about the Fractionary
Schr\"{o}dinger 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's function for a free particle in the general
case, for an arbitrary order of the derivative index.Comment: 32 pages. No figure
Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature
Frieden and Soffer conjectured some years ago the existence of a ``Fisher
temperature" T_F that would play, with regards to Fisher's information measure
I, the same role that the ordinary temperature T plays vis-a-vis Shannon's
logarithmic measure. Here we exhibit the existence of reciprocity relations
between T_F and T and provide an interpretation with reference to the meaning
of T_F for the canonical ensemble.Comment: 3 pages, no figure
Inversion of Tsallis' q-Fourier Transform and the complex-plane generalization
We introduce a complex q-Fourier transform as a generalization of the (real)
one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered
ultradistributions we show that this complex plane-generalization overcomes all
troubles that afflict its real counterpart.Comment: 23 pages, no figure
Power-law random walks
We present some new results about the distribution of a random walk whose
independent steps follow a Gaussian distribution with exponent
. In the case we show that a stochastic
representation of the point reached after steps of the walk can be
expressed explicitly for all . In the case we show that the random
walk can be interpreted as a projection of an isotropic random walk, i.e. a
random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure
On the connection between Complementarity and Uncertainty Principles in the Mach-Zehnder interferometric setting
We revisit, in the framework of Mach-Zehnder interferometry, the connection
between the complementarity and uncertainty principles of quantum mechanics.
Specifically, we show that, for a pair of suitably chosen observables, the
trade-off relation between the complementary path information and fringe
visibility is equivalent to the uncertainty relation given by Schr\"odinger
and Robertson, and to the one provided by Landau and Pollak as well. We also
employ entropic uncertainty relations (based on R\'enyi entropic measures) and
study their meaning for different values of the entropic parameter. We show
that these different values define regimes which yield qualitatively different
information concerning the system, in agreement with findings of [A. Luis,
Phys. Rev. A 84, 034101 (2011)]. We find that there exists a regime for which
the entropic uncertinty relations can be used as criteria to pinpoint non
trivial states of minimum uncertainty.Comment: 7 pages, 2 figure
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