Abstract
We obtain a distribution of Fermi-Dirac type for a hard liquid at temperatures less than the Frenkel temperature T F for P ≥ 0 and Z ≥ 0. For the van der Waals model, one has T F = (33/25)T c .
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V. P. Maslov, “Undistinguishing statistics of objectively distinguishable objects: Thermodynamics and superfluidity of classical gas,” Math. Notes 94(5–6), 722–813 (2013).
V. P. Maslov, “Two-fluid picture of supercritical phenomena,” Teoret. Mat. Fiz. 180(3), 394–432 (2014) [Theoret. and Math. Phys. 180 (3), 1096–1129 (2014)].
V. P. Maslov, “New parastatistics leading to classical thermodynamics: Physical interpretation,” Math. Notes 96(1–2), 50–67 (2014).
V. P. Maslov, “On new ideal (noninteracting) gases in supercritical thermodynamics,” Mat. Zametki 97(1), 85–102 (2015) [Math. Notes 97 (1–2), 85–99 (2015)].
H. Poincaré, About Science (Nauka, Moscow, 1983) [in Russian].
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London-Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).
V. P. Maslov, “On the semiclassical transition in the quantum Gibbs distribution,” Math. Notes 97(3–4), 565–574 (2015).
“The Russian Federation National Award in Science and Technology is conferred to Maslov Viktor Pavlovich,” Teor. Veroyatnost. Primenen. 59(2), 209–213 (2014).
B. B. Kadomtsev, Collective Phenomena in Plasma (Nauka, Moscow, 1988) [in Russian].
L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian].
A. N. Shiryaev, Probability, Vol. 1: Elementary Probability Theory. Mathematical Foundations. Limit Theorems (MCCME, Moscow, 2004) [in Russian].
B. B. Kadomtsev, “Dynamics and Information,” Uspekhi Fiz. Nauk, 1999).
V. P. Maslov, “On the number of eigenvalues for a Gibbs ensemble of self-adjoint operators,” Mat. Zametki 83(3), 465–467 (2008) [Math. Notes 83 (3–4), 424–427 (2008)].
V. P. Maslov, “Gibbs and Bose-Einstein distributions for an ensemble of self-adjoint operators in classical mechanics,” Teoret. Mat. Fiz. 155(2), 312–316 (2008) [Theoret. and Math. Phys. 155 (2), 775–779 (2008)].
V. P. Maslov, “Gas-amorphous solid and liquid-amorphous solid phase transitions. Introduction of negative mass and pressure from the mathematical viewpoint,” Math. Notes 97(3–4), 423–430 (2015).
I. A. Kvasnikov, Thermodynamics and Statistical Physics: Theory of Equilibrium Systems (URSS, Moscow, 2002), Vol. 2 [in Russian].
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Maslov, V.P. Probability distribution for a hard liquid. Math Notes 97, 909–918 (2015). https://doi.org/10.1134/S0001434615050259
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DOI: https://doi.org/10.1134/S0001434615050259