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On the spectral gap in the region of negative pressures
Mathematical notes. 2016. Vol. 99. No. 5. P. 711–714.
Maslov V. P., Maslov A. V.
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 for μ < 0. This term is the right-hand side of the Fermi–Dirac distribution. In this paper, it is also shown how to find the “liquid–amorphous body” binodal.
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
Maslov V. P., 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
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
Maslov V. P., 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. ...
Added: December 7, 2016
Maslov V. P., Mathematical notes 2016 Vol. 100 No. 1 P. 154–185
The author constructs a new conception of thermodynamics which is based on new results in number theory. We consider a maximally wide range of gases, liquids, and fluids to which, in principle, the Carathéodory approach can be applied. The Carathéodory principle is studied using the Lennard-Jones potential as an example. On the basis of this ...
Added: October 10, 2016
Maslov V., 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.. ...
Added: September 7, 2015
Maslov V. P., 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
Maslov V. P., , 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
Maslov V. P., 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
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
The boundary of a volume as a trap ensuring the phase transition in an ideal gas at low temperatures
Maslov V. P., 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
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