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physica status solidi (b)

Fisher information and quantum–classical field theory: classical statistics similarity

Jacek Syska

Published May 10, 2007• 10 citations
Publisher

Abstract

Abstract The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self‐consistent field theory, which joins the quantum theory and classical field theory, is proposed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200674646

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Abstract The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self‐consistent field theory, which joins the quantum theory and classical field theory, is proposed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The master equation case and structural information principle are derived. Then, the phenomenological description of the information transfer is presented. The extreme physical information (EPI) method is reviewed. As if marginal, the statistical interpretation of the amplitude of the system is given. The formalism developed in this paper would be also applied in quantum information processing and quantum game theory (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Abstract We show an approximate method to calculate the polarizability of a many‐electron system within Green's function theory in a similar way as within time‐dependent density functional theory (TDDFT). The basic idea is to join the computational simplicity of the latter with the accuracy of the former. We apply this approach to a prototype system, LiF. For comparison, we also show results obtained within other approximated TDDFT‐based methods. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
It is shown that Schrödinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared, and some fundamental differences are identified.