105 research outputs found
On a conjecture regarding Fisher information
Fisher's information measure plays a very important role in diverse areas of
theoretical physics. The associated measures as functionals of quantum
probability distributions defined in, respectively, coordinate and momentum
spaces, are the protagonists of our present considerations. The product of them
has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A
(2000) 62 012107]. We show here that such is not the case. This is illustrated,
in particular, for pure states that are solutions to the free-particle
Schr\"odinger equation. In fact, we construct a family of counterexamples to
the conjecture, corresponding to time-dependent solutions of the free-particle
Schr\"odinger equation. We also give a new conjecture regarding any
normalizable time-dependent solution of this equation.Comment: 4 pages; revised equations, results unchange
Comment on "Quantum discord through the generalized entropy in bipartite quantum states"
In [X.-W. Hou, Z.-P. Huang, S. Chen, Eur. Phys. J. D 68, 1 (2014)], Hou et
al. present, using Tsallis' entropy, possible generalizations of the quantum
discord measure, finding original results. As for the mutual informations and
discord, we show here that these two types of quantifiers can take negative
values. In the two qubits instance we further determine in which regions they
are non-negative. Additionally, we study alternative generalizations on the
basis of R\'enyi entropies.Comment: 5 pages, 4 figure
Noise versus chaos in a causal Fisher-Shannon plane
We revisit the Fisher-Shannon representation plane , evaluated using the Bandt and Pompe recipe to assign a
probability distribution to a time series. Several stochastic dynamical (noises
with , , power spectrum) and chaotic processes (27 chaotic
maps) are analyzed so as to illustrate the approach. Our main achievement is
uncovering the informational properties of the planar location.Comment: 6 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1401.213
Pattern Recognition In Non-Kolmogorovian Structures
We present a generalization of the problem of pattern recognition to
arbitrary probabilistic models. This version deals with the problem of
recognizing an individual pattern among a family of different species or
classes of objects which obey probabilistic laws which do not comply with
Kolmogorov's axioms. We show that such a scenario accommodates many important
examples, and in particular, we provide a rigorous definition of the classical
and the quantum pattern recognition problems, respectively. Our framework
allows for the introduction of non-trivial correlations (as entanglement or
discord) between the different species involved, opening the door to a new way
of harnessing these physical resources for solving pattern recognition
problems. Finally, we present some examples and discuss the computational
complexity of the quantum pattern recognition problem, showing that the most
important quantum computation algorithms can be described as non-Kolmogorovian
pattern recognition problems
Statistical Mechanics-based Schrodinger treatment of Gravity
The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via E = mc2 . In the case of axions, this perspective has been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641]. Therein, a simple Schrödinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde’s entropic force advanced in [Physica A 511 (2018) 139]. In this paper, we revisit this technique with regards to fermions’ behavior (specifically, baryons).Fil: Plastino, Angelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Social Thermodynamics Applied Research; SuizaFil: Rocca, Mario Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin
Thermodynamics of firms' growth
The distribution of firms' growth and firms' sizes is a topic under intense
scrutiny. In this paper we show that a thermodynamic model based on the Maximum
Entropy Principle, with dynamical prior information, can be constructed that
adequately describes the dynamics and distribution of firms' growth. Our
theoretical framework is tested against a comprehensive data-base of Spanish
firms, which covers to a very large extent Spain's economic activity with a
total of 1,155,142 firms evolving along a full decade. We show that the
empirical exponent of Pareto's law, a rule often observed in the rank
distribution of large-size firms, is explained by the capacity of the economic
system for creating/destroying firms, and can be used to measure the health of
a capitalist-based economy. Indeed, our model predicts that when the exponent
is larger that 1, creation of firms is favored; when it is smaller that 1,
destruction of firms is favored instead; and when it equals 1 (matching Zipf's
law), the system is in a full macroeconomic equilibrium, entailing "free"
creation and/or destruction of firms. For medium and smaller firm-sizes, the
dynamical regime changes; the whole distribution can no longer be fitted to a
single simple analytic form and numerical prediction is required. Our model
constitutes the basis of a full predictive framework for the economic evolution
of an ensemble of firms that can be potentially used to develop simulations and
test hypothetical scenarios, as economic crisis or the response to specific
policy measures
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