Application of a Quantum Ensemble Model to Linguistic Analysis

A new set of parameters to describe the word frequency behavior of texts is proposed. The analogy between the word frequency distribution and the Bose-distribution is suggested and the notion of “temperature” is introduced for this case. The calculations are made for English, Ukrainian, and the Guinean Maninka languages. The correlation between in-deep language structure (the level of analyticity) and the defined parameters is shown to exist.

💡 Research Summary

The paper “Application of a Quantum Ensemble Model to Linguistic Analysis” proposes a novel statistical framework for describing word‑frequency distributions in natural language texts by borrowing concepts from quantum statistical mechanics, specifically the Bose‑Einstein (BE) distribution. The authors argue that traditional models such as Zipf’s law or the Zipf‑Mandelbrot extension capture the heavy‑tailed nature of word frequencies only in a limited way; they often fail to account for the pronounced “condensation” of high‑frequency words and the long tail of rare words simultaneously. To address this, the authors map linguistic quantities onto physical analogues: each distinct word type is treated as a quantum energy level (εi), the number of occurrences of that word as the occupation number (ni), and they introduce two thermodynamic‑like parameters – a chemical potential (μ) and a temperature (T). The BE occupation formula

  ni = 1 /