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Maslov distribution and formulas for the entropy. (English) Zbl 1252.80001

Summary: The Maslov distribution for a system of identical particles is used. The entropy and some other thermodynamical characteristics of this system are found for diverse fractal dimensions. A general formula for the entropy is established, which shows that the entropy is proportional to the derivative of the system energy with respect to the temperature. It is shown that a parastatistical parameter \(b\), which is introduced formally, is related to the temperature of the system indeed. The nature of the phase transition in the system is studied in the two-dimensional case.

MSC:

80A05 Foundations of thermodynamics and heat transfer
80A10 Classical and relativistic thermodynamics
82B03 Foundations of equilibrium statistical mechanics
82B05 Classical equilibrium statistical mechanics (general)
80M35 Asymptotic analysis for problems in thermodynamics and heat transfer
28A78 Hausdorff and packing measures
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References:

[1] V. P. Maslov, ”Threshold Levels in Economics,” ArXiv:0903.4783v2, 3 Apr 2009. · Zbl 1179.91214
[2] V. P. Maslov, ”New Look at Thermodynamics of Gas and at Clusterization,” Russ. J. Math. Phys. 15(4), 493–510 (2008). · Zbl 1180.80005 · doi:10.1134/S1061920808040079
[3] V. P. Maslov, ”Theory of Chaos and Its Application to the Crisis of Debts and the Origin of the Inflation,” Russ. J. Math. Phys. 16(1), 103–120 (2009). · Zbl 1179.91207 · doi:10.1134/S1061920809010087
[4] V. P. Maslov, ”On an Ideal Gas Related to the Law of Corresponding States,” Russ. J. Math. Phys. 17(2), 240–250 (2010). · Zbl 1267.82123 · doi:10.1134/S1061920810020081
[5] I. A. Kvasnikov, Thermodynamics and Statistical Physics. Theory of Equilibrium Systems (URSS, Moscow, 2002) [in Russian].
[6] L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1964, 2001; Pergamon Press, Oxford, 1968). · Zbl 0859.76001
[7] V. P. Maslov and V. E. Nazaikinskii, ”On the Distribution of Integer Random Variables Related by a Certain Linear Inequality: I,” Mat. Zametki 83(2), 232–263 (2008) [Math. Notes 83 (1–2), 211–237 (2008)]. · Zbl 1150.82017 · doi:10.4213/mzm4418
[8] E. Jahnke, F. Emde, and F. Lösch, Tafeln höherer Funktionen (B. G. Teubner Verlagsgesellschaft, Stuttgart, 1966).
[9] I. A. Kvasnikov, Thermodynamics and Statistical Physics (Izd-vo MGU, Moscow, 1991) [in Russian].
[10] V. P. Maslov, ”The {\(\lambda\)}-Point in Helium-4 and Nonholonomic Clusters,” Math. Notes 87(2), 298–300 (2010). · Zbl 1198.82064 · doi:10.1134/S0001434610010396
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