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New Parastatistics Leading to Classical Thermodynamics: Physical Interpretation
Mathematical notes. 2014. Vol. 96. No. 1. P. 50-67.
This paper presents UD-statistics almost coinciding with Gentile statistics for negative chemical potentials, but having another extension in the case of positive chemical potentials. The physical meaning of the metamorphosis of the phase transition of the third kind to the phase transition of the first kind is explained. The coincidence of isochores and isotherms in the supercritical domain corresponding to UD statistics is shown.
49606783, Mathematical notes 2014 Vol. 96 No. 3 P. 403-415
In this paper, we refine some of the original notions, such as the number of degrees of freedom, for an arbitrary temperature
and an ideal Boltzmann--Maxwell gas. Using the van der Waals model, we illustrate the notion of Frenkel temperature,
which separates soft and rigid liquid. ...
Added: December 21, 2014
49606783, Mathematical notes 2014 Vol. 95 No. 5 P. 3-18
In this paper, a new approach to the two-body problem is considered in greater detail than in previous papers of the author.
The semiclassical transition from quantum statistics to classical statistics is studied and an analog of superfluidity
in classical thermodynamics for supercritical states is obtained. ...
Added: December 21, 2014
49606783, Mathematical notes 2014 Vol. 95 No. 1 P. 91-97
We consider various normalizations enabling us to change the scale of the graphs of isotherms and isochores. The relationship between parastatisticsal value of the maximal number of particles, corresponding to a given energy, and temperature allows us to pass in the domain of positive chemical potentials from the parastatisticsal number K (K = ∞ corresponds ...
Added: June 5, 2014
49606783, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 2 P. 256-284
We consider the main ideas that led the author to the construction of the new
thermodynamics; this construction explains the Gibbs paradox and the new experimental effects of supercritical thermodynamics, as well as the law of preference of cluster formation before passage of gases to the liquid state. The law of invariance of the fractional number ...
Added: November 30, 2014
49606783, Mathematical notes 2014 Vol. 95 No. 3 P. 399-406
Undistinguishing parastatistics of objectively distinguishable objects is considered. It describes clusters in the supercritical state. The relationship between the mesoscopic physics of clusters and the macroscopic thermodynamics of supercritical isotherms is established. We construct the supercritical pattern of isochores and isotherms under the assumption that the following three points: the Boyle temperature, the Boyle density, and the critical ...
Added: December 20, 2014
Maslov V., Теоретическая и математическая физика 2014 Т. 180 № 3 С. 394-432
We consider a parastatistics that does not distinguish objectively different objects but describes clusters in the supercritical state and determines the relation between the mesoscopic physics of clusters and the macroscopic thermodynamics of supercritical isotherms. We construct the supercritical picture of isochores and isotherms under the condition that the Boyle temperature, the Boyle density, and ...
Added: October 26, 2014
49606783, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 1 P. 99-111
In the article, the relationship between the mesoscopic picture and the microscopic and macroscopic pictures is considered in the light of the work of V. E. Panin and his school. The coincidence of isochores and isotherms obtained by applying the undistinguishing statistics of objectively distinguishable objects with those of the Van-der-Waals model allows us to ...
Added: June 5, 2014
49606783, Mathematical notes 2014 Vol. 96 No. 5 P. 732-738
For UD-statistics, we present formulas that are in agreement with the value of the second virial coefficient as $\rho\to 0$
at the initial point of the activity a\to 0 and with the temperature on the critical isochore rho=\rho_c at the final point.
This leads to two invariants: (1) the number of collective degrees of freedom and 2) ...
Added: December 24, 2014
49606783, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 4 P. 494-503
In this paper, general questions concerning equilibrium and non-equilibrium states are discussed. Using the Van-der-Waals model, the relationship between Gentile statistics and non-ideal gas is demonstrated. The second virial coefficient is expressed in terms of collective degrees of freedom. The admissible cluster size at given temperature is determined. ...
Added: November 30, 2014
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
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, Maslova T. V., Russian Journal of Mathematical Physics 2014 Vol. 21 No. 3 P. 373-378
Boyle temperature is interpreted as the temperature at which the formation of dimers becomes impossible. To Irving Fisher's correspondence principle we assign two more quantities: the number of degrees of freedom, and credit. We determine the danger level of the mass of money M when the mutual trust between economic agents begins to fall. ...
Added: November 30, 2014
49606783, Maslova T. V., Mathematical notes 2014 Vol. 95 No. 6 P. 881-885
After the work of Irving Fisher, who formulated the main law of economics as an analog of the Claiperon--Clausius--Mendeleev relation corresponding to the Boltzmann--Maxwell ideal gas, the authors have developed this approach on the basis of the general principles of UD-statistics by assigning to the nominal interest rate the role of the chemical potential mu ...
Added: December 21, 2014
Ulyanov V. V., Bobkov S., Danshina M., / CRC 1283, Bielefeld University, Bielefeld, Germany. Series 21027 "Collaborative Research Centre 1283, Bielefeld University". 2021. No. 21027.
Convergence of order O(1/ √ n) is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in generalized random graphs with random vertex weights. The weights are assumed to be independent identically distributed random variables which have a power-law distribution. The proof is ...
Added: March 29, 2021
49606783, Russian Journal of Mathematical Physics 2017 Vol. 24 No. 4 P. 495-504
This paper presents a new approach to thermodynamics based on two “first
principles”: the theory of partitions of integers and Earth gravitation. The self-correlated
equation obtained by the author from Gentile statistics is used to describe the effect of
accumulation of energy at the moment of passage from the boson branch of the partition to
its fermion branch. The ...
Added: November 17, 2018
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 2019 Vol. 26 No. 3 P. 352-367
In this paper, a new physical notion, intensity, is introduced.
The notion of intensity occurs in a special statistics, known as Gentile statistics, which
is asymptotically close to ordinary thermodynamics. The introduction
of the new notion of intensity in the theory of nuclear matter
essentially changes the thermodynamical picture. Moreover, we can
say that the thermodynamics of nuclear matter is ...
Added: August 25, 2019
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, Mathematical notes 2017 Vol. 102 No. 2 P. 234-251
It is shown in the paper that the number pN(M) of partitions of a positive integer M
into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic
accuracy if one identifies M with energy and N with the number of particles. We use the Gentile
statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that ...
Added: October 29, 2018
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
49606783, Mathematical notes 2018 Vol. 103 No. 2 P. 316-318
In view of the results obtained in this communication we can connect macroscopy and microscopy via an intermediate level of mesoobjects. ...
Added: December 8, 2018
49606783, Mathematical notes 2018 Vol. 103 No. 6 P. 929-935
It is well known that the formula for the Fermi distribution is obtained from the formula
for the Bose distribution if the argument of the polylogarithm, the activity a, the energy, and the
number of particles change sign. The paper deals with the behavior of the Bose–Einstein distribution
as a → 0; in particular, the neighborhood of the ...
Added: December 8, 2018
Талипова Т. Г., Kurkina O. E., Giniyatullin A. et al., Экологические системы и приборы 2013 № 12 С. 17-25
The surface-active substances everywhere are presented on the water surface, they are exposed to waves and currents, and are involved in the processes of ocean-atmosphere exchange. They play a prominent role in the formation of small-scale part of the spectrum of wind waves and affect the manifestations of internal waves on the sea surface. In ...
Added: November 18, 2013
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020