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

Legendre-transform structure derived from quantum theorems

Datos recopilados de la publicación electrónica.Texto completo arXiv:1101.4661By recourse to (i) the Hellmann–Feynman theorem and (ii) the virial one, the information-optimizing principle based on Fisher’s information measure uncovers a Legendre-transform structure associated with Schrödinger’s equation, in close analogy with the structure that lies behind the standard thermodynamical formalism. The present developments provide new evidence for the information theoretical links based on Fisher’s measure that exist between Schrödinger’s equation, on the one hand, and thermodynamics/thermostatistics on the other hand.This work has been partially supported by the Programs FQM-2445 and FQM-207 of the Junta de AndaluciaPeer reviewe

The workings of the maximum entropy principle in collective human behaviour

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996-2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.Instituto de Física La Plat

The workings of the maximum entropy principle in collective human behaviour

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996-2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.Instituto de Física La Plat

Erratum: Connection between entanglement and the speed of quantum evolution

PACS number s : 03.67.Mn, 89.70. c, 03.65. w, 02.50. r, 99.10.CdErratum: Connection between entanglement and the speed of quantum evolution [Phys. Rev. A 72, 032337 (2005)]Peer reviewe

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.Instituto de Física La Plat

Numerical determination of the distribution of energies for the XY-model

4 pages, 1 figure.-- PACS: 05.20.−y; 05.50.+q; 05.70.Ce; 75.10.HkPre-print archive.-- ArXiv pre-print: http://arxiv.org/abs/cond-mat/0109141We compute numerically the distribution of energies $Omega(E,N)$ for the XY--model with short--range and long--range interactions. We find that in both cases the distribution can be fitted to the functional form: $Omega(E,N)sim exp(N phi(E,N))$, with $phi(E,N)$ an intensive function of the energy.We acknowledge financial support from DGES (Spain) project PB97-0141-C02-01 and MCyT (Spain) project BMF2000-0624.Peer reviewe

Nonextensive thermostatistics and the H theorem

Using the Boltzmann's transport equation method, the kinetic foundations of Tsallis' nonextensive thermostatistics were investigated. The analysis follows from a nonextensive generalization of the 'molecular chaos hypothesis.' For q > 0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.Fil: Lima, J.A.. Universidade Federal do Rio Grande do Norte; BrasilFil: Silva, R.. Universidade Federal do Rio Grande do Norte; BrasilFil: Plastino, Ángel Ricardo. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Universitat de les Illes Balears; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentin

Multiqubit systems: highly entangled states and entanglement distribution

Texto completo arXiv:0803.3979v1.-- PACS: 03.67.Lx Quantum computation architectures and implementations 03.67.Mn Entanglement measures, witnesses, and other characterizations 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).-A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also exploredThis work was partially supported by the MEC grant FIS2005-02796 (Spain) and FEDER (EU) and by CONICET (Argentine Agency). The financial assistance of the National Research Foundation (NRF; South African Agency) toward this research is hereby acknowledged. Opinions expressed and conclusions arrived at, are those of the authors and are not necessarily to be attributed to the NRF. A Borras acknowledges support from the FPU grant AP-2004- ´ 2962 (MEC-Spain)Peer reviewe

Multispecies effects in the equilibrium and out-of-equilibrium thermostatistics of overdamped motion

Progress has been recently made, both theoretical and experimental, regarding the thermostatistics of complex systems of interacting particles or agents (species) obeying a nonlinear Fokker-Planck dynamics. However, major advances along these lines have been restricted to systems consisting of only one type of species. The aim of the present contribution is to overcome that limitation, going beyond single-species scenarios. We investigate the dynamics of overdamped motion in interacting and confined many-body systems having two or more species that experience different intra- A nd interspecific forces in a regime where forces arising from standard thermal noise can be neglected. Even though these forces are neglected, the behavior of the system can be analyzed in terms of an appropriate thermostatistical formalism. By recourse to a mean-field treatment, we derive a set of coupled nonlinear Fokker-Planck equations governing the behavior of these systems. We obtain an H theorem for this Fokker-Planck dynamics and discuss in detail an example admitting an exact, analytical stationary solution.Fil: Plastino, Ángel Ricardo. Universidad Nacional del Noroeste de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nobre, F. D.. Centro Brasileiro de Pesquisas Físicas; BrasilFil: Wedemann, R. S.. Universidade do Estado de Rio do Janeiro; Brasi