What's the big idea? Cramér–Rao inequality and Rao distance

Angel Ricardo Plastino and Angelo Plastino give a brief introduction to two key developments in statistics that originate with C. R. Rao's 1945 paper, “Information and accuracy attainable in the estimation of statistical parameters”.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Pergamino); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plastino, Ángel Ricardo. 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

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

Robe's restricted three-body problem revisited

Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.Facultad de Ciencias Astronómicas y Geofísica

Tsallis entropy and Jaynes' Information Theory formalism

The role of Tsalli's non-extensive Information Measure within an a la Jaynes Information-Theory-based formulation of Statistical Mechanics is discussed in rather detailed fashion.Facultad de Ciencias ExactasConsejo Nacional de Investigaciones Científicas y Técnica

Revisiting entanglement within the Bohmian approach to quantum mechanics

We revisit the concept of entanglement within the Bohmian approach to quantum mechanics. Inspired by Bohmian dynamics, we introduce two partial measures for the amount of entanglement corresponding to a pure state of a pair of quantum particles. One of these measures is associated with the statistical correlations exhibited by the joint probability density of the two Bohmian particles in configuration space. The other partial measure corresponds to the correlations associated with the phase of the joint wave function, and describes the non-separability of the Bohmian velocity field. The sum of these two components is equal to the total entanglement of the joint quantum state, as measured by the linear entropy of the single-particle reduced density matrix.Fil: Zander, Claudia. University of Pretoria; SudáfricaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentin

Tsallis entropy and the Vlasov-Poisson equations

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravitational N-body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following considerations we shall be dealing witha D-dimensional space so as to be in a position to investigate possible dimensional dependences of Tsallis' parameter q. The particular and important case of the Schuster solution is studied in detail, and the pertinent Tsallis parameter q is given as a function of the space dimension. In the special case of three dimensional space we recover the value q = 7/9, that has already appeared in many applications of Tsallis' formalism involving long range forces.Facultad de Ciencias Astronómicas y GeofísicasFacultad de Ciencias Exacta

Heating, Cooling, and Equilibration of an Interacting Many-Fermion System

We discuss the process of equilibrium?s attainment in an interacting many fermionssystem linked to a heat reservoir, whose temperature T is subject toa short-time disturbance of total duration 2τ . In this time-interval, its temperatureincreases up to a maximum value M T , cooling off afterward (alsogradually) to its original value. The process is described by a typical masterequation that leads eventually to equilibration. We discuss how the equilibrationprocess depends upon 1) the system?s fermion-number, 2) the fermion-fermioninteraction?s strength V, 3) the disturbance duration 2τ , and finally4) the maximum number of equations N of the master equation.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ferri, Gustavo Luis. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Plastino, Ángel Ricardo. 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

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

Magic Numbers and Mixing Degree in Many-Fermion Systems

We consider an N fermion system at low temperature T in which we encounter special particle number values (Formula presented.) exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the (Formula presented.). For a quantum state described by the matrix (Formula presented.), its purity is expressed by (Formula presented.) and then the degree of mixture is given by (Formula presented.), a quantity that coincides with the entropy (Formula presented.) for (Formula presented.). Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.Fil: Monteoliva, D.. Universidad Nacional de La Plata; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; 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; ArgentinaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentin

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