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

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.