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Dec 1998

Volume 39, Issue 12, pp. 6247-6756

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Information gain within nonextensive thermostatistics

Lisa Borland, Angel R. Plastino, and Constantino Tsallis

J. Math. Phys. 39, 6490 (1998); http://dx.doi.org/10.1063/1.532660 (12 pages) | Cited 46 times

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Show Abstract
We discuss the information theoretical foundations of the Kullback information gain, recently generalized within a nonextensive thermostatistical formalism. General properties are studied and, in particular, a consistent test for measuring the degree of correlation between random variables is proposed. In addition, minimum entropy distributions are discussed and the H-theorem is proved within the generalized context. © 1998 American Institute of Physics.
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics
05.70.Ce Thermodynamic functions and equations of state

The quantum canonical ensemble

Dorje C. Brody and Lane P. Hughston

J. Math. Phys. 39, 6502 (1998); http://dx.doi.org/10.1063/1.532661 (7 pages) | Cited 10 times

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The phase space Γ of quantum mechanics can be viewed as the complex projective space CPn endowed with a Kählerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrödinger equation as generating a Hamiltonian dynamics on Γ. Based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles. The resulting density matrix for the canonical Γ-ensemble differs from the density matrix of the conventional approach. As an illustration, the results are applied to the case of a spin one-half particle in a heat bath with an applied magnetic field. © 1998 American Institute of Physics.
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05.30.Ch Quantum ensemble theory

Dirichlet forms and Dirichlet operators for infinite particle systems: Essential self-adjointness

Veni Choi, Yong Moon Park, and Hyun Jae Yoo

J. Math. Phys. 39, 6509 (1998); http://dx.doi.org/10.1063/1.532662 (28 pages) | Cited 2 times

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We study the Dirichlet forms and the associated Dirichlet operators for Gibbs measures on infinite particle configuration space. The Dirichlet forms are defined to be “gradient-type” forms by introducing a measurable field of rigged Hilbert spaces on the configuration space. Under mild conditions on the interaction including singular potentials, we show that the pre-Dirichlet operator is symmetric and that the closure of the pre-Dirichlet form satisfies the Markovian property. When the interaction is three times differentiable and decreasing sub-exponentially, we show that the Dirichlet operator is essentially self-adjoint on a domain consisting of bounded smooth local functions. © 1998 American Institute of Physics.
Show PACS
05.70.Ce Thermodynamic functions and equations of state
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.30.Hq Ordinary differential equations
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