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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.
49606783, 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, ...
Added: May 22, 2017
49606783, Mathematical notes 2013 Vol. 94 No. 5 P. 722-813
In the present paper, we describe an approach to thermodynamics that does not involve Bogolyubov chains or Gibbs ensembles. We present isotherms, isochores, and isobars of various pure gases, as well as binodals, i.e., lines along which gas becomes liquid, and spinodals (endpoints of isotherms). We study supercritical phenomena for values of temperature and pressure ...
Added: December 23, 2013
49606783, 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 ...
Added: September 21, 2016
49606783, , in : Reference Module in Earth Systems and Environmental Sciences. : Oxford : Elsevier, 2014. Ch. 64. P. 1-11.
The relationship between thermodynamics and economics has been known for a long time. The term ``thermoeconomics'' has even appeared. However, several aspects of the old thermodynamics are unacceptable in economics. For example, experts in thermodynamics believe that the diamond crystal is in the metastable state, and in due time will be transformed into graphite. However, ...
Added: March 27, 2014
Kondo S., Chida M., Yamuchi T., K-Theory 2014 Vol. 14 No. 2 P. 313-342
We compute the rational K_2 group of an elliptic surface over a finite field in terms of the order of zeros of the associated L-function. ...
Added: March 15, 2015
49606783, Mathematical notes 2016 Vol. 100 No. 5 P. 886-889
Added: February 21, 2017
Beilinson A., Kings G., Andrey Levin, / Cornell University. Series math "arxiv.org". 2014.
We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for GL_n(Z) and yields classes with values in an Iwasawa algebra. This implies directly the integrality properties of special values of L-functions of totally real fields and a construction of the associated p-adic L-function. Using a result of Graf, we ...
Added: February 5, 2015
Kondo S., Yasuda S., / Cornell University. Series math "arxiv.org". 2014.
We study the homology and the Borel-Moore homology with coefficients in Q of a quotient (called arithmetic quotient) of the Bruhat-Tits building of PGL of a nonarchimedean local field of positive characteristic by an arithmetic subgroup (a special case of the general definition in Harder's article (Invent.\ Math.\ 42, 135-175 (1977)). We define an analogue ...
Added: December 11, 2014
49606783, , in : Advances in Chemistry Research. Vol. 21.: NY : Nova Science Publishers, 2014. Ch. 6. P. 197-219.
We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in ...
Added: February 24, 2014
Maslov V., Mathematical notes 2012 Vol. 92 No. 3 P. 402-411
Negative pressure also means negative energy and, therefore, “holes”, antiparticles. Continuation across infinity to negative energies is accomplished by using a parastatistical correction to the Bose-Einstein distribution. ...
Added: January 17, 2013
Maslov V., Baddiredy A., Aoki Y. et al., NY : Nova Science Publishers, 2014
We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in ...
Added: November 18, 2013
Maslov V., 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, ...
Added: October 8, 2015
Idrisova V. A., Tokareva N. N., Gorodilova A. A. et al., Prikladnaya Diskretnaya Matematika 2023 No. 62 P. 29-54
Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The main goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in ...
Added: March 19, 2024
The boundary of a volume as a trap ensuring the phase transition in an ideal gas at low temperatures
49606783, Mathematical notes 2012 Vol. 92 No. 5-6 P. 657-663
It is shown that reflection from the boundary of a volume containing a gas plays a significant role in the occurrence of the second phase, and the corresponding correction (related to this effect) to the results obtained by the author in previous papers dealing with the theory of the new ideal gas is given. ...
Added: February 12, 2013
I. V. Kolokolov, V. V. Lebedev, Tumakova M. M., Journal of Experimental and Theoretical Physics 2023 Vol. 136 No. 6 P. 785-794
We investigate fluctuations of vorticity inside a coherent vortex generated by the inverse energy cascade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair correlation function. The interaction of fluctuations leads to a nonzero third moment of vorticity. We analyze the
pair correlation function and the third moment using a model in ...
Added: June 8, 2023
Maslov V., Теоретическая и математическая физика 2015 Т. 182 № 2 С. 365-367
In contrast to the supercritical region where the isotherms ideally coincide with the isotherms of the van
der Waals model, we introduce an additional condition for the Hartley entropy to attain maximum on the
spinodal in the subcritical region. To determine the parameters of the distribution and isotherms, we use
spinodal equation. ...
Added: March 8, 2017
49606783, 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. ...
Added: February 21, 2017
Negodin V., Polyachenko Y., Fleita D. et al., Journal of Molecular Liquids 2021 Vol. 322 No. 1-3 Article 114954
The equilibrium and metastable states of the Lennard-Jones vapor, liquid, and crystal, are studied in the vicinity of the phase transition points. Vapor-liquid, liquid-vapor, liquid-crystal, and crystal-liquid transitions are modeled within the molecular dynamics method. As a research tool, a four-point correlation function is used for the qualitative detection of collective motions of atoms in ...
Added: May 14, 2021
49606783, Mathematical notes 2017 Vol. 101 No. 3 P. 488-496
Abstract—Regularization of the Bose–Einstein distribution using a parastatistical correction,
i.e., by means of the Gentile statistics, is carried out. It is shown that the regularization result
asymptotically coincides with the Erdo˝ s formula obtained by using Ramanujan’s formula for the
number of variants of the partition of an integer into summands. TheHartley entropy regarded as the
logarithm of the ...
Added: October 28, 2018
Maslov V., Mathematical notes 2013 Vol. 94 No. 4 P. 532-546
It is well known that the supercritical state of a gas has great dissolving capacity. In this paper, the mathematical reason for this phenomenon is studied in great detail. ...
Added: November 18, 2013
49606783, Russian Journal of Mathematical Physics 2015 Vol. 22 No. 1 P. 53-67
We provide a detailed explanation of the physical meaning of some concepts used in the new statistics corresponding to thermodynamics, including the notions of locally ideal gas, number of collective degrees of freedom, and jamming factor. The equation of state is treated as a surface in three-dimensional space, and the spinodal is viewed as an ...
Added: March 8, 2015
Kalmynin A. B., Konyagin S., / Cornell University. Series math "arxiv.org". 2023. No. 2303.14833.
Added: November 22, 2023
Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660-665
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...
Added: October 28, 2018
49606783, Russian Journal of Mathematical Physics 2017 Vol. 24 No. 2 P. 249-260
In the paper, the problem of partitioning a natural number into summands is considered in connection with the BKT (Berezinskii–Kosterlitz–Thouless) phase transition and its two critical points. As examples, the passage from superfluid state to normal state and from a cell-like vortical state to turbulent state are considered. ...
Added: November 17, 2018