Inferring an optimal Fisher measure

It is well known that a suggestive relation exists that links the Schrödinger equation (SE) to the information-optimizing principle based on the Fisher information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.Fil: Flego, Silvana Pilar. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Ciencias Básicas; ArgentinaFil: Plastino, Ángel Luis. 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. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Universidad de las Islas Baleares; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Centro Regional de Estudios Genómicos; Argentina. Universidad de Granada. Facultad de Ciencias. Departamento de Electromagnetismo y Física de la Materia. Instituto "Carlos I" de Física Teórica y Computacional; Españ

Quantum field theory, Feynman-, Wheeler propagators, dimensional regularization in configuration space and convolution of Lorentz invariant tempered distributions

The Dimensional Regularization (DR) of Bollini and Giambiagi (BG) can not be defined for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S'L. In this paper we overcome such limitation and show that it can be generalized to all aforementioned STDELI and obtain a product in a ring with zero divisors. For this purpose, we resort to a formula obtained by Bollini and Rocca and demonstrate the existence of the convolution (in Minkowskian space) of such distributions. This is done by following a procedure similar to that used so as to define a general convolution between the Ultradistributions of J Sebastiao e Silva (JSS), also known as Ultrahyperfunctions, obtained by Bollini et al. Using the Inverse Fourier Transform we get the ring with zero divisors S'LA, defined as S'LA = F-1 {S'L}, where F-1 denotes the Inverse Fourier Transform. In this manner we effect a dimensional regularization in momentum space (the ring S'L) via convolution, and a product of distributions in the corresponding configuration space (the ring S'LA). This generalizes the results obtained by BG for Euclidean space. We provide several examples of the application of our new results in Quantum Field Theory (QFT). In particular, the convolution of n massless Feynman’s propagators and the convolution of n massless Wheeler’s propagators in Minkowskian space. The results obtained in this work have already allowed us to calculate the classical partition function of Newtonian gravity, for the first time ever, in the Gibbs’ formulation and in the Tsallis’ one. It is our hope that this convolution will allow one to quantize non-renormalizable Quantum Field Theories (QFT’s).Fil: Plastino, Ángel Luis. 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; ArgentinaFil: 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; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

Fluctuations, entropic quantifiers and classical-quantum transition

We show that a special entropic quantifier, called the statistical complexity, becomes maximal at the transition between super-Poisson and sub-Poisson regimes. This acquires important connotations given the fact that these regimes are usually associated with, respectively, classical and quantum processes.Fil: Pennini, Flavia Catalina. 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. Universidad Católica del Norte. Departamento de Física; ChileFil: Plastino, Ángel Luis. 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

Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs' statistical mechanics

Appealing to the 1902 Gibbs formalism for classical statistical mechanics (SM)-the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics-we show that already at the classical level there is a strong correlation between Renyi's exponent α and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.Fil: Plastino, Ángel Luis. 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; ArgentinaFil: 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

Legendre transform structure and extremal properties of the relative Fisher information

Variational extremization of the relative Fisher information (RFI, hereafter) is performed. Reciprocity relations, akin to those of thermodynamics are derived, employing the extremal results of mthe RFI expressed in terms of probability amplitudes. A time independent Schrodinger-like equation (Schrodinger like link) for the RFI is derived. The concomitant Legendre transform structure (LTS hereafter) is developed by utilizing a generalized RFI-Euler theorem, which shows that the entire mathematical structure of htermodynamics translates into the RFI framework, both for equilibrium and non equilibrium cases. The qualitatevily distinct nature of the present results visd-a-vis those of prio studies utilizing the Shannon Entropy and/or the Fisher information mmeasure is discussed. A principled relationship between the RFI and the FIM ferameworks is derived. The utility of this relationship is demosnstrated by an example wherein the energy eigenvalues of the Schroedinger-like link for the RFI are inferred solely using the quantum mechanical virial theorem and the LTS of the RFI.Fil: Venkatesan, R. C.. Systems Research Corporation; IndiaFil: Plastino, Ángel Luis. 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

Editorial: Entropic aspects of nonlinear partial differential equations: Classical and quantum mechanical perspectives

There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies. It is well known that some fundamental partial differential equations of applied mathematics and of mathematical physics—such as the linear diffusion equation—are closely linked to the standard, logarithmic Boltzmann–Gibbs–Shannon–Jaynes entropic measure.Facultad de Ciencias Exacta

Quantum entanglement in a many-body system exhibiting multiple quantum phase transitions

We investigate the quantum entanglement-related features of the many-body model of Plastino and Moszkowski [N. Cimento 47 (1978) 470]. This is an exactly solvable N-body, SU2 two-level model exhibiting several quantum phase transitions. We show that these transitions happen to be also entanglement-transitions associated with different many-body Dicke states. The main properties of the model considered here make it particularly well suited to study, by recourse to exact analytical computations, some connections between quantum phase transitions and quantum entanglement-theory.Facultad de Ciencias Exacta

Inferring an optimal Fisher measure

It is well known that a suggestive relation exists that links the Schrödinger equation (SE) to the information-optimizing principle based on the Fisher information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.Facultad de IngenieríaInstituto de Física La PlataCentro Regional de Estudios Genómico

Information theory consequences of the scale-invariance of Schröedinger's equation

In this communication we show that Fisher's information measure emerges as a direct consequence of the scale-invariance of Schröedinger's equation. Interesting, well-known additional results are re-obtained as well, for whose derivation only (and this is the novelty) the scale invariance property is needed, without further ado.Facultad de Ciencias Exacta

Inferring an optimal Fisher measure

It is well known that a suggestive relation exists that links the Schrödinger equation (SE) to the information-optimizing principle based on the Fisher information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.Facultad de IngenieríaInstituto de Física La PlataCentro Regional de Estudios Genómico