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Transform information: A symmetry breaking measure

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Abstract

A connection between two fundamental concepts of information and symmetry breaking (SB) is established. A concept called transform information (TI) is introduced. The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures). As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as a quantitative SB measure in the system under study. The classical information measures that are derived from TI also can be perceived as SB measures. This fact is a base for assigning a sense to information. The concept of TI is extended to the cases when systems are described without the use of probability concept.

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  1. VST Laboratories, Ivanteevskaya St., 1-1-39, Moscow, 107150, Russia

    G. V. Vstovsky

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Vstovsky, G.V. Transform information: A symmetry breaking measure. Found Phys 27, 1413–1444 (1997). https://doi.org/10.1007/BF02551520

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