Menzerath-Altmann Law: Statistical Mechanical Interpretation as Applied to a Linguistic Organization

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EROĞLU S.

JOURNAL OF STATISTICAL PHYSICS, vol.157, no.2, pp.392-405, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 157 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.1007/s10955-014-1078-8
  • Journal Name: JOURNAL OF STATISTICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.392-405
  • Keywords: Semiotic sequences, Self-organization, Collective phenomena, Boltzmann distribution, Model generalization, Statistical inference, LANGUAGE, GENOMES, SIZE, TEXT
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

The distribution behavior described by the empirical Menzerath-Altmann law is frequently encountered during the self-organization of linguistic and non-linguistic natural organizations at various structural levels. This study presents a statistical mechanical derivation of the law based on the analogy between the classical particles of a statistical mechanical organization and the distinct words of a textual organization. The derived model, a transformed (generalized) form of the Menzerath-Altmann model, was termed as the statistical mechanical Menzerath-Altmann model. The derived model allows interpreting the model parameters in terms of physical concepts. We also propose that many organizations presenting the Menzerath-Altmann law behavior, whether linguistic or not, can be methodically examined by the transformed distribution model through the properly defined structure-dependent parameter and the energy associated states.