763 research outputs found
Reciprocity relations and generalized entropic quantifiers that lack trace-form
In this effort we show that the Legendre reciprocity
relations,thermodynamic's essential formal feature, are respected by any
entropic functional, even if it is NOT of trace-form nature, as Shannon's is.
Further, with reference to the MaXent variational process, we encounter
important cases, relevant to physical applications currently discussed in the
research literature, in which the associated reciprocity relations exhibit
anomalies. We show that these anomalies can be cured by carefully
discriminating between apparently equivalent entropic forms
Inclusion relations among separability criteria
We revisit the application of different separability criteria by recourse to
an exhaustive Monte Carlo exploration involving the pertinent state-space of
pure and mixed states. The corresponding chain of implications of different
criteria is in such a way numerically elucidated. We also quantify, for a
bipartite system of arbitrary dimension, the proportion of states that
can be distilled according to a definite criterion. Our work can be regarded as
a complement to the recent review paper by B. Terhal [Theor. Comp. Sci. {\bf
287} (2002) 313]. Some questions posed there receive an answer here.Comment: Submitted for publicatio
Properties of a geometric measure for quantum discord
We discuss some properties of the quantum discord based on the geometric
distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {\bf 105},
190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how
good the measure is in representing quantum discord. We explore the dependence
of quantum discord on the degree of mixedness of the bipartite states, and also
its connection with non-locality as measured by the maximum violation of a Bell
inequality within the CHSH scenario
Jensen-Shannon divergence, Fisher information, and Wootters' hypothesis
We discuss different statistical distances in probability space, with
emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert
space and their relationship with Fisher's information measure. This study
provides further reconfirmation of Wootters' hypothesis concerning the
possibility that statistical fluctuations in the outcomes of measurements be
regarded (at least partly) as responsible for the Hilbert-space structure of
quantum mechanics
General Solution of a Fractional Diffusion-Advection Equation for Solar Cosmic-Ray Transport
In this effort we exactly solve the fractional diffusion-advection equation
for solar cosmic-ray transport proposed in \cite{LE2014} and give its {\it
general solution} in terms of hypergeometric distributions. Also, we regain all
the results and approximations given in \cite{LE2014} as {\it particular cases}
of our general solution.Comment: 12 pages, no figure
Hypergeometric Connotations of Quantum Equations
We show that the Schr\"odinger and Klein-Gordon equations can both be derived
from an Hypergeometric differential equation. The same applies to non linear
generalizations of these equations.Comment: 16 pages, no figure
On the entropic derivation of the Newtonian gravity force
Following Verlinde's conjecture, we show that Tsallis' classical free
particle distribution at temperature can generate Newton's gravitational
force's {\it distance's dependence}. If we want to repeat the
concomitant argument by appealing to either Boltzmann-Gibbs' or Renyi's
distributions, the attempt fails and one needs to modify the conjecture.
Keywords: Tsallis', Boltzmann-Gibbs', and Renyi's distributions, classical
partition function, entropic force.Comment: 10 pages. No figure
Possible Divergences in Tsallis' Thermostatistics
Trying to compute the nonextensive q-partition function for the Harmonic
Oscillator in more than two dimensions, one encounters that it diverges, which
poses a serious threat to the whole of Tsallis' thermostatistics. Appeal to the
so called q-Laplace Transform, where the q-exponential function plays the role
of the ordinary exponential, is seen to save the day.Comment: Text has change
Hypergeometric foundations of Fokker-Plank like equations
We show that the Fokker Planck equation can be derived from a Hypergeometric
differential equation. The same applies to a non linear generalization of such
equation.Comment: 9 pages. No figure
Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture
Verlinde conjectured eight years ago that gravitation might be an emergent
entropic force. This rather surprising assertion was proved in [Physica A {\bf
505} (2018) 190] within a purely classical statistical context, and in [DOI:
10.13140/RG.2.2.34454.24640] for the case of bosons' statistics. In the present
work, we appeal to a quantum scenario involving fermions' statistics. We
consider also the classical limit of quantum (statistical) mechanics (QM). We
encounter a lower bound to the distance between the two interacting masses,
i.e., an cut-off. This is a new effect that exhibits some resemblance with
the idea of space discretization proposed by recent gravitation theoriesComment: 10 pages, 2 figure
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