Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy

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dc.creatorNiven, Robert K.
dc.date2005-12-01
dc.date2007-04-20
dc.date.accessioned2026-07-07T08:15:10Z
dc.date.available2026-07-07T08:15:10Z
dc.descriptionThis study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three bases, since it gives (i) a derivation for the Kullback-Leibler cross-entropy and Shannon entropy functions, as simplified forms of the multinomial distribution subject to the Stirling approximation; (ii) an explanation for the need to maximize entropy (or minimize cross-entropy) to find the most probable realization; and (iii) new, generalized definitions of entropy and cross-entropy - supersets of the Boltzmann principle - applicable to non-multinomial systems. The combinatorial basis is therefore of much broader scope, with far greater power of application, than the information-theoretic and axiomatic bases. The generalized definitions underpin a new discipline of ``{\it combinatorial information theory}'', for the analysis of probabilistic systems of any type. Jaynes' generic formulation of statistical mechanics for multinomial systems is re-examined in light of the combinatorial approach. (abbreviated abstract)
dc.description45 pp; 1 figure; REVTex; updated version 5 (incremental changes)
dc.identifierhttps://arxiv.org/abs/cond-mat/0512017
dc.identifierhttp://arxiv.org/abs/cond-mat/0512017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133368
dc.subjectStatistical Mechanics
dc.subjectInformation Theory
dc.subjectMathematical Physics
dc.subjectData Analysis, Statistics and Probability
dc.titleCombinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy
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