Abstract:
In this article, we study, from the mathematical point of view, the analogies between language and multi-particle systems in thermodynamics. We attempt to introduce an appropriate mathematical apparatus and the technical tools of statistical physics to descriptions of language. In particular, we apply the notions of number of degrees of freedom, Bose condensate, phase transition and others to linguistics objects. On the basis of a statistical analysis of dictionaries and statistical distributions in languages, we conjecture that the transition from the semiotic communication system of the higher primates to human language can be described as a phase transition of the first kind. We show that the number of words appearing with frequency 1 in a corpus of texts is equal to the number of ones in the corresponding Fermi–Dirac distribution, while the high frequency of stop-words corresponds to the large number of particles in the Bose condensate, when the number of degrees of freedom is less than two, provided there is a gap in the spectrum. The presented considerations are illustrated by examples from the Russian language. Some of the illustrative examples are untranslatable into English, and so they were replaced in translation by similar examples from the English language.
Keywords:
number of degrees of freedom, frequency of occurrence, frequency dictionary, Zipf law, statistical language distribution, Bose–Einstein distribution, Fermi–Dirac distribution, number theory, Van-der-Waals model, isotherm, tropical topology, tropical analysis, telegraphic style, stop-word.
Citation:
V. P. Maslov, “The Relationship between the Fermi–Dirac Distribution and Statistical Distributions in Languages”, Mat. Zametki, 101:4 (2017), 531–548; Math. Notes, 101:4 (2017), 645–659
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\by V.~P.~Maslov
\paper The Relationship between the Fermi--Dirac Distribution and Statistical Distributions in Languages
\jour Mat. Zametki
\yr 2017
\vol 101
\issue 4
\pages 531--548
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\crossref{https://doi.org/10.4213/mzm11531}
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\transl
\jour Math. Notes
\yr 2017
\vol 101
\issue 4
\pages 645--659
\crossref{https://doi.org/10.1134/S0001434617030221}
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Linking options:
https://www.mathnet.ru/eng/mzm11531
https://doi.org/10.4213/mzm11531
https://www.mathnet.ru/eng/mzm/v101/i4/p531
This publication is cited in the following 9 articles:
Ch.-Ch. Zhou, Yu.-Zh. Chen, W.-Sh. Dai, “Unified framework for generalized statistics: canonical partition function, maximum occupation number, and permutation phase of wave function”, J. Stat. Phys., 186:1 (2022), 19
A. A. Lebedev, N. V. Maksimov, “Analogies between physics and information processing”, Autom. Doc. Math. Linguist., 54:5 (2020), 233–242
V. P. Maslov, “Motivation and Essence of the Term “tropical Mathematics””, Russ. J. Math. Phys., 27:4 (2020), 478–483
A.A. Lebedev, A.A. Lebedev, N.V. Maksimov, N.V. Maksimov, “Analogii v fizike i obrabotke informatsii”, Nauchno-tekhnicheskaya informatsiya. Seriya 2: Informatsionnye protsessy i sistemy, 2020, no. 10, 1
Ch.-Ch. Zhou, W.-Sh. Dai, “Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases”, J. Stat. Mech. Theory Exp., 2018, no. 2, 023105, 31 pp.
Ch.-Ch. Zhou, W.-Sh., “Calculating eigenvalues of many-body systems from partition functions”, J. Stat. Mech. Theory Exp., 2018, 083103, 24 pp.
Ch.-Ch. Zhou, W.-Sh. Dai, “A statistical mechanical approach to restricted integer partition functions”, J. Stat. Mech. Theory Exp., 2018, no. 5, 053111, 25 pp.
V. P. Maslov, T. V. Maslova, “A generalized number theory problem applied to ideal liquids and to terminological lexis”, Russ. J. Math. Phys., 24:1 (2017), 96–110
V. P. Maslov, “Remarks on Number Theory and Thermodynamics Underlying Statistical Distributions in Languages”, Math. Notes, 101:4 (2017), 660–665
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