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

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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.

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Notes

  1. Henceforth, we will refer to vocabulary of a text as distinct words (DWs) for convenience. In general, DWs of a text can be considered as the set of dissimilar constituents of a construct at the level of organization under investigation.

  2. Thus, we will use the terminologies word length and word energy interchangeably, for the rest of the paper.

  3. Note that we only consider the word length distribution of DWs in a text, so the frequency and the occurrence positions of the constituents (words) are insignificant.

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Acknowledgments

We are grateful to A. Algin for helpful discussions and we appreciate the careful proofreading of the manuscript by H. Kreuzer. This work was partially supported by Eskisehir Osmangazi University’s Scientific Research Project Commission (Grant No. 2008-19019).

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Authors and Affiliations

  1. Department of Physics, Eskisehir Osmangazi University, Meselik, 26480, Eskisehir, Turkey

    Sertac Eroglu

  2. Department of Biotechnology and Biosafety, Graduate School of Natural and Applied Sciences, Eskisehir Osmangazi University, Meselik, 26480, Eskisehir, Turkey

    Sertac Eroglu

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Eroglu, S. Menzerath–Altmann Law: Statistical Mechanical Interpretation as Applied to a Linguistic Organization. J Stat Phys 157, 392–405 (2014). https://doi.org/10.1007/s10955-014-1078-8

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  • DOI: https://doi.org/10.1007/s10955-014-1078-8

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