Modern thermodynamics as a branch of mathematics (mathematical physics)

V. P. Maslov

doi:10.1134/S0001434616090078

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Modern thermodynamics as a branch of mathematics (mathematical physics)

Mathematical notes. 2016. Vol. 100. No. 3. P. 413–420.

A parallel between physical derivation and mathematical proof in classical thermodynamics is drawn. A relationship between thermodynamics and analytic number theory is demonstrated.

Язык: английский

DOI

Ключевые слова: spinodal binodal number theory equilibrium state fluctuation metastable state spouting effect

Mathematical problems and solutions of the Ninth International Olympiad in Cryptography NSUCRYPTO

Idrisova V. A., Tokareva N. N., Gorodilova A. A. и др., Prikladnaya Diskretnaya Matematika 2023 No. 62 P. 29–54

Добавлено: 19 марта 2024 г.

Large gaps between sums of two squareful numbers

Калмынин А. Б., Konyagin S., / Series math "arxiv.org". 2023. No. 2303.14833.

Добавлено: 22 ноября 2023 г.

Correlations of Vorticity inside a Coherent Vortex

I. V. Kolokolov, V. V. Lebedev, Tumakova M. M., Journal of Experimental and Theoretical Physics 2023 Vol. 136 No. 6 P. 785–794

Добавлено: 8 июня 2023 г.

Kinetic singularities at transition points from equilibrium to metastable states of the Lennard-Jones particle system

Negodin V., Polyachenko Y., Флейта Д. Ю. и др., Journal of Molecular Liquids 2021 Vol. 322 No. 1-3 Article 114954

Добавлено: 14 мая 2021 г.

Topological Phase Transitions in the Theory of Partitions of Integers

, Russian Journal of Mathematical Physics 2017 Vol. 24 No. 2 P. 249–260

Добавлено: 17 ноября 2018 г.

A Generalization of a Classical Number-Theoretic Problem, Condensate of Zeros, and Phase Transition to an Amorphous Solid

, Mathematical notes 2017 Vol. 101 No. 3 P. 488–496

Добавлено: 28 октября 2018 г.

Remarks on Number Theory and Thermodynamics Underlying Statistical Distributions in Languages

Маслов В. П., Mathematical notes 2017 Vol. 101 No. 4 P. 660–665

Добавлено: 28 октября 2018 г.

The Fermi-Dirac distribution as a model of a thermodynamically ideal liquid. Phase transition of the first kind for neutral gases (corresponding to nonpolar molecules)

, Mathematical notes 2017 Vol. 101 No. 1 P. 100–114

In this paper, we introduce the notions of enlarged number theory and of thermodynamically ideal liquid and calculate the temperature below which it appears. This temperature is T = 0.84Tc, where Tc is the critical temperature of a gas whose molecules are nonpolar. For such a gas, in a sufficiently wide neighborhood of the binodal, ...

Добавлено: 22 мая 2017 г.

UD-статистика в подкритической области

Маслов В. П., Теоретическая и математическая физика 2015 Т. 182 № 2 С. 365–367

В подкритической области, в отличие от суперкритической, в которой изотермы идеально совпадают с изотермами модели Ван-дер-Ваальса, введено дополнительное условие достижения максимума энтропии Хартли на спинодали. Для определения параметров распределения и изотерм используется уравнение спинодали. ...

Добавлено: 8 марта 2017 г.

Volume and entropy in abstract analytic number theory and thermodynamics

, Dobrokhotov S. Y., Nazaikinskii V. E., Mathematical notes 2016 Vol. 100 No. 5 P. 828–834

We develop the recent research [1] and introduce the notions of volume and entropy in abstract analytic number theory. The introduction of negative numbers in the generalized partition problem, together with the meaning of such a generalization in some applications of the theory, is discussed. ...

Добавлено: 21 февраля 2017 г.

Tropical topology

, Mathematical notes 2016 Vol. 100 No. 5 P. 886–889

Добавлено: 21 февраля 2017 г.

On the spectral gap in the region of negative pressures

, Maslov A. V., Mathematical notes 2016 Vol. 99 No. 5 P. 711–714

It is shown that, between the values of the activity a = 1 and a < 1, there is a gap, which can be overcome by using additional energy. This energy is defined on the spinodal a = 1 (μ = 0) on theP–Z diagram and gives, in the parastatistical distribution, an additional term of Bose condensate type, which is also preserved ...

Добавлено: 21 сентября 2016 г.

Locally ideal liquid

Маслов В. П., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 3 P. 361–373

The notion of locally ideal liquid, similar to locally ideal fluid, is introduced. The distribution of locally ideal liquid is presented and compared with the one given by the van der Waals equation. The notion of phase transition from the metastable liquid state to the metastable solid state (glass) is introduced. © 2015, Pleiades Publishing, ...

Добавлено: 8 октября 2015 г.

Probability distribution for a hard liquid

Маслов В. П., Mathematical notes 2015 Vol. 97 No. 5-6 P. 909–918

We obtain a distribution of Fermi-Dirac type for a hard liquid at temperatures less than the Frenkel temperature TF for P ≥ 0 and Z ≥ 0. For the van der Waals model, one has TF = (33/25)Tc. © 2015, Pleiades Publishing, Ltd. ...

Добавлено: 7 сентября 2015 г.

Statistics Corresponding to Classical Thermodynamics. Construction of Isotherms

, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 1 P. 53–67

Добавлено: 8 марта 2015 г.

Topological polylogarithms and p-adic interpolation of L-values of totally real fields

Beilinson A., Kings G., Andrey Levin, / Series math "arxiv.org". 2014.

Добавлено: 5 февраля 2015 г.

The Borel-Moore homology of an arithmetic quotient of the Bruhat-Tits building of PGL of a non-archimedean local field in positive characteristic and modular symbols

Кондо С., Yasuda S., / Series math "arxiv.org". 2014.

Добавлено: 11 декабря 2014 г.

Thermodynamics and Economics: Overview

, , in: Reference Module in Earth Systems and Environmental Sciences.: Oxford: Elsevier, 2014. Ch. 64 P. 1–11.

Добавлено: 27 марта 2014 г.