Undistinguishing statistics of objectively distinguishable objects: Thermodynamics and superfluidity of classical gas

V. V. Kozlov, Thermal Equilibrium According to Gibbs and Poincaré (Institute for Computer Studies,, Moscow, 2002) [in Russian].

The European Physical Journal 37(4) (2012).

V. A. Malyshev and R. A. Minlos, Gibbs Random Fields: Cluster Expansions Mathematics and Its Applications (Kluwer Academic Publishers, Dordrecht-Boston, 1991).

A. A. Lykov and V. A. Malyshev, “Convergence to Gibbs equilibrium-unveiling the mystery,” Markov Processes and Related Fields 19(4) (2013).

A. M. Vershik, “Statistical mechanics of combinatorial partitions, and their limit shapes,” Funktsional. Anal. Prilozhen. 30(2), 19–39 (1996) [Functional Anal. Appl. 30 (2), 90–105 (1996)].

V. P. Maslov, “Quasithermodynamics and a correction to the Stefan-Boltzmann law,” Mat. Zametki 83(1), 77–85 (2008) [Math. Notes 83 (1) 72–79 (2008)].

V. P. Maslov, “Quasithermodynamic correction to the Stefan-Boltzmann law,” Teoret. Mat. Fiz. 154(1), 207–208 (2008) [Theoret. and Math. Phys. 154 (1), 175–176 (2008)].

H.-O. Georgii, GibbsMeasures and Phase Transitions (Walter de Gruyter, Berlin, 2011).

D. Ruelle, Statistical Mechanics (W. A. Benjamin, Inc., New York-Amsterdam, 1969; Mir, Moscow, 1971).

Ya. G. Sinai, Theory of Phase Transitions (Nauka, Moscow, 1980).

B. Ya. Frenkel, Yakov Il’ich Frenkel (Nauka Publ., Moscow-Leningrad, 1966) [in Russian].

V. P. Maslov, “On a Serious Mathematical Error in the “Mathematical Encyclopedia” Related to the Solution of the Gibbs Paradox,” Math. Notes 93(5), 732–739 (2013).

V. P. Maslov, “Old Mathematical Errors in Statistical Physics,” Russian J. Math. Phys. 20(2), 214–229 (2013).

V. P. Maslov, “The Law of Preference of Cluster Formation over Passage to Liquid State,” Math. Notes 94(1) 115–126 (2013).

V. P. Maslov, “The Law of Preference of Cluster Formation over Passage to Liquid State II,” Math. Notes 94(3) 364–368 (2013).

L. D. Landau and E.M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian].

Mathematical Encyclopedia (Soviet Encyclopedia, Moscow, 1984), Vol. 4 [in Russian].

W.-S. Dai and M. Xie, “Gentile statistics with a large maximum occupation number,” Annals of Physics 309, 295–305 (2004).

V. P. Maslov, Thermodynamics as a Multistep Relaxation Process and the Role of Observables in Different Scales of Quantities, arXiv:1303.5307v2 [physics.gen-ph], 25 Mar 2013.

V. P. Maslov, “Unbounded Probability Theory and Multistep Relaxation Processes,” Math. Notes 93(3) 451–459 (2013).

V. P. Maslov, “On I.M. Gelfand’s 100th Anniversary,” Math. Notes 94(6), 841–842 (2013).

V. P. Maslov, Threshold Levels in Economics, arXiv:0903.4783v2 [q-fin.ST] 3 Apr 2009.

V.P. Maslov, Daring to Touch Radha (Academic Express, Lviv, 1993); also on http://viktor.maslovs.co.uk/en/home/articles/hist/my-hist .

A. I. Anselm, Foundations of Statistical Physics and Thermodynamics (Nauka, Moscow, 1973) [in Russian].

H. Eyring, Basic Chemical Kinetics (Mir, Moscow, 1985) [in Russian].

L. I. Mandelshtam and M. A. Leontovich, “On the theory of absorption of sound in liquid,” Zh. Éksp. Teoret. Fiz. 7(3), 438–449 (1937)

V. P. Maslov, Quantization of Thermodynamics and Ultrasecond Quantization (Institute for Computer Studies, Moscow, 2001) [in Russian].

S. T. Kuroda, “Scattering theory for differential operators. III,” Lecture Notes in Mathematics 448, 227–241 (1975).

G. A. Martynov, Fundamental theory of liquids: method of distribution functions, (A. Hilger, Bristol-Philadelphia-New York, 1992).

G. L. Litvinov, “Maslov dequantization, idempotent and tropicalmathematics: a brief introduction,” Journal of Math. Sciences 140(3), 426–444 (2007).

E. M. Apfelbaum, V. S. Vorob’ev, “Correspondence between the critical and the Zeno-line parameters for classical and quantum liquids,” J.Phys.Chem. B 113, 3521–3526 (2009).

V. P. Maslov, “Thermodynamics of fluids: The law of redestribution of energy, two-dimensional condensate, and T-mapping,” Teoret.Mat. Fiz. 161(3), 422–456 (2009) [Theoret. and Math. Phys. 161 (3), 1681–1713 (2009)].

E. M. Apfelbaum, V. S. Vorobtev, and G. A. Martynov,, “Triangle of Liquid-Gas States,” J. Phys. Chem. B 110, 8474–8480 (2006).

V. P. Maslov, “Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential: I,” Math. Notes 86(3–4), 522–529 (2009).

V. P. Maslov, “Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential: II (the law of redistribution of energies),” Math. Notes 86(5–6), 605–611 (2009).

V. P. Maslov, “Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential: III,” Math. Notes 87(1–2), 79–87 (2010).

V. P. Maslov, “The mathematical theory of classical thermodynamics,” Math. Notes 93(1) 102–136 (2013).

V.P. Maslov, “Mixture of new ideal gases and the solution of problems in Gibbs and Einstein paradoxes,” Russian J. Math. Phys. 18(1), 83–101 (2011).

G. Birkhoff, Hydrodynamics (Princeton, 1950; Inostr. Lit., Moscow, 1954).

W.-G. Dong and J. Lienhard, “Corresponding states correlation of saturated and metastable properties,” Canadian J. Chem. Eng. 64, 158–161 (1986).

V. P. Maslov and P. P. Mosolov, Nonlinear Wave Equations Perturbed by Viscous Term, De Gruyter Expositions in Mathematics 31 (Walter de Gruyter, Berlin-New York, 2000).

S. M. Stishov and A. V. Smirnov, “Study of expanded substance at low temperature by the Monte-Carlo method,” Pis’ma Zh. Éksp. Teoret. Fiz. 57(11), 715–720 (1993).

R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals (New York, 1965; Mir, Moscow, 1968).

V. P. Maslov, Perturbation Theory and Asymptotical Methods (Izd. Moskov. Univ., Moscow, 1965; Dunod, Paris, 1972) [in Russian and French].

N. Hurt, Geometric Quantization in Action (Reidel, Dordrecht, 1983; Mir,Moscow, 1985).

V. P. Maslov, Asymptotic Methods and Perturbation Theory (Nauka, Moscow,1988) [in Russian].

V. P. Maslov, “Nonstandard characteristics in asymptotic problems,” Uspekhi Mat. Nauk 38(6), 3–36 (1983).

L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantu 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. V. Brazhkin, A. G. Lyapin, V. N. Ryzhov, K. Trachenko, Yu. D. Fomin, and E. N. Tsiok, “Where is the supercritical fluid on the phase diagram?” Uspekhi Fiz. Nauk 182(11), 1137–1156 (2012) [Physics-Uspekhi 55 (11), 1061–1079 (2012)].

E. M. Apfelbaumand V. S. Vorob’ev, “Regarding the universality of some consequences of the van der Waals equation in the supercritical domain,” Journ. Phys. Chem. B 117(25), 7750–7755 (2013).

E. M. Apfelbaum and V. S. Vorob’ev, “The saturation pressure for different objects in reduced variables and the justification of some empirical relations set from the van der Waals equation,” Chem. Phys. Lett. (2013) (in press).

V. P. Maslov, “Critical indices as a consequence of Wiener quantization of thermodynamics,” Teoret. Mat. Fiz. 170(3), 458–470 (2012) [Theoret. and Math. Phys. 170 (3), 384–393 (2012)].

D. Yu. Ivanov, Critical Behavior of Non-Ideal Systems (Fizmatlit, Moscow, 2003; Wiley-VCH, 2008).

V. P. Maslov, “A mathematical theory of the supercritical state serving as an effective means of destruction of chemical warfare agents,” Math. Notes 94(4) 532–546 (2013).

V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov, and K. Trachenko, “Universal crossover of liquid dynamics in supercritical region,” Pis’ma Zh. Eksp.Teor.Fiz. 95(3), 179–184 (2012)

V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov, and K. Trachenko, “Two liquid states of matter: A dynamic line on a phase diagram,” Phys. Rev. E 85(3), 031203–215 (2012).

V. V. Brazhkin, Yu. D. Fomin, A. G. Lyapin, V. N. Ryzhov, E. N. Tsiok, and K. Trachenko, “Liquid-Gas” Transition in the Supercritical Region: Fundamental Changes in the Particle Dynamics,” Phys. Rev. Lett. 111(14), 145901–905 (2013).

A.M. Stishov, “Phase transition in expanded matter,” Pis’ma Zh. Eksp.Teor.Fiz. 57(3) 189–194 (1993)

V. P. Maslov and T. V. Maslova, “Economics as an analog of thermodynamics: conjugate variables,” Math. Notes 91(3) 442–444 (2012).

V. P. Maslov, “Quasi-particles associated with Lagrangian manifolds corresponding to semiclassical self consistent fields. III,” Russian J. Math. Phys., 3(2) 271–276 (1995).

V. P. Maslov and O. Yu. Shvedov, The Complex Germ Method in Many-Particle Problems and in Quantum Field Theory (Editorial URSS, Moscow, 2000) [in Russian]

V. P. Maslov, The Complex WKB Method in Nonlinear Equations (Nauka, Moscow, 1977) [in Russian].

A. A. Vlasov, “On the vibrational properties of an electronic gas,” Zh. Éxper. Teoret. Fiz. 8, 291–238 (1938).

Mathematical Encyclopedic Dictionary (Soviet Encyclopedia, Moscow, 1988) [in Russian].

Ph. Blanchard and M. Sirugue, “Large deviations from classical paths,” Comm. Math. Phys. 101, 173–185 (1985).

V. P. Maslov, Complex Markov Chains and the Feynman Path Integral for Nonlinear Equations (Nauka, Moscow, 1976) [in Russian].

V. P. Maslov and O. Yu. Shvedov, “An asymptotic formula for the N-particle density function as N →∞ and a violation of the chaos hypothesis,” Russ. J. Math. Phys. 2(2), 217–234 (1994).

V. P. Maslov and P. P. Mosolov, “Asymptotic behavior as N →∞ of trajectories of N point masses interacting according to Newton’s gravitation law,” Izv. Akad. Nauk SSSR Ser. Mat. 42(5), 1063–1100 (1978).

V. P. Maslov, “Quasiparticles associated with Lagrangian manifolds and corresponding to classical selfconsistent fields. II,” Russ. J. Math. Phys. 3(1), 123–132 (1995).

V. P. Maslov and O. Yu. Shvedov, “Quantization in the neighborhood of classical solution in the N-particle problem and superfluidity,” Theoret. and Math. Phys. 98(2), 181–196 (1994).

V. P. Maslov, O. Yu. Shvedov, “Complex WKB-method in the Fock space,” Doklady Akad. Nauk 340(1), 42–47 (1995).

V. P. Maslov and O. Yu. Shvedov, “Large deviations in the many-body problem,” Mat. Zametki 57(1), 133–137 (1995).

V. P. Maslov, “Mathematical aspects of weakly nonideal Bose and Fermi gases on a crystal base,” Funktsional. Anal. i Prilozhen. 37(2), 16–27 (2003) [Functional Anal. Appl. 37 (2), (2003)].

V. P. Maslov, “A note on computer-oriented language,” Problemy Peredachi Informatsii 39(3),72–76 (2003).

V. P. Maslov, “Spectral series and quantization of thermodynamics,” Russ. J. Math. Phys. 9(1), 112–122 (2002).

V. P. Maslov, “A model of weakly nonideal Bose gas. Phase transition in superfluid state spouting effect,” Vestnik Moskov. Univ. Ser. Fiz. Astron. 1, 3–11 (2003).

V. P. Maslov, “Quasi-particles associated with Lagrangian manifolds corresponding to semiclassical self-consistent fields. IV,” Russian J. Math. Phys. 3(3), 401–406 (1995).

V. P. Maslov, “Quasi-particles associated with Lagrangian manifolds corresponding to semiclassical self-consistent fields. V-XI,” Russian J. Math. Phys. 3, 529–534 (1995); 4, 117–122, 265–270, 539–546 (1996); 5, 123–130, 273–278, 405–412 (1997).

V. P. Maslov, “Analytic continuation of asymptotic formulas and axiomatic foundations of thermodynamics and quasithermodynamics,” Functional Anal. Appl. 28(4), 28–41 (1994).

N. N. Bogolyubov, On the Theory of Superfluidity, in Selected Works (Naukova Dumka, Kiev, 1970), Vol. 2 [in Russian].

V. P. Maslov, “Spectral series, superfluidity, and high-temperature superconductivity,” Mat. Zametki 58(6), 933–936 (1995) [Math. Notes 58 (6), 1349–1352 (1995)].

V. P. Maslov, “Spectral series and quantization of thermodynamics,” Russian J. Math. Phys. 9(1), 112–122 (2002).

Physical Encyclopedic Dictionary (Sovetskaya Entsiklopediya, Moscow, 1966), Vol. 5 [in Russian].

V. P. Maslov, “On the dispersion law of the form $$\varepsilon (p) = \hbar ^2 p^2 /2m + \tilde V(p) - \tilde V(0)$$ for elementary excitations of a nonideal Fermi gas in the pair interaction approximation (i ↔ j), V (|x i − x j|),” Mat. Zametki 82(5), 690–708 (2007) [Math. Notes 82 (5), 619–634 (2007)].

F. A. Berezin, The Method of Second Quantization (Nauka, Moscow, 1987) [in Russian].

L. D. Landau, “On the theory of superfluidity,” in Collected Papers (Nauka, Moscow, 1969), Vol. 2, pp. 42–46 [in Russian].

V. P. Maslov, “On the appearance of the λ-point in a weakly nonideal Bose gas and the two-liquid Thiess-Landau model,” Russian J. Math. Phys. 16(2), 146–165 (2009).

V. P. Maslov, “On the Bose condensate in the two-dimensional case, λ-point and the Thiess-Landau twoliquid model,” Teoret. Mat. Fiz. 159(1), 20–23 (2009).

V. P. Maslov, “Generalization of the second quantization method to the case of special tensor products of Fock space and quantization of free energy,” Funktsional. Anal. Prilozhen. 34(4), 35–48 (2000).

V. P. Maslov, “Supersecond quantization and quantization of entropy with preserved charge,” UspekhiMat. Nauk 55(6), 145–146 (2000).

V. P. Maslov, “Some identities for ultrasecond-quantized operators,” Russ. J. Math. Phys. 8(3), 309–321 (2001).

V. P. Maslov, “Quantization of thermodynamics, ultrasecondary quantization and a new variational principle,” Russ. J. Math. Phys. 8(1), 55–82 (2001)

V. P. Maslov, “Ultratertiary quantization of thermodynamics,” Teoret. Mat. Fiz. 132(3), 388–398 (2002) [Theoret. and Math. Phys. 132 (3), 1222–1232 (2002)].

E. M. Lifshits and L. P. Pitaevskii, Statistical Physics, Part 2: Theory of Condensed State (Nauka, Moscow, 1978; Pergamon, Oxford, 1980).

V. P. Maslov, “On the dependence of the criterion for superfluidity from the radius of the capillary,” Teoret. Mat. Fiz. 143(3), 307–327 (2005) [Theoret. and Math. Phys. 143 (3), 741–759 (2005)].

V. P. Maslov, “Resonance between one-particle (Bogolyubov) and two-particle series in a superfluid liquid in a capillary,” Russ. J. Math. Phys. 12(3), 369–379 (2005).

V. P. Maslov, “The scattering problem in the quasiclassical approximation,” Dokl. Akad. Nauk SSSR 151, 306–309 (1963) [Soviet Physics Dokl. 8, 666–668 (1964)].

Yu. S. Barash, Van der Waals Forces (Nauka, Moscow, 1988) [in Russian].

V. P. Maslov, “Quantization of Boltzmann entropy, pairs, and the correlation function,” Teoret. Mat. Fiz. 131(2), 261–277 (2002) [Theoret. and Math. Phys. 131 (2), 666–680 (2002)].

V. P. Maslov, “On the averaging method for a large number of clusters. Phase transitions,” Teoret. Mat. Fiz. 125(2), 297–314 (2000) [Theoret. and Math. Phys. 125 (2), 1552—1567 (2000)].

V. P. Maslov, “Ultrasecond quantization and ‘ghosts’ in quantized entropy,” Teoret. Mat. Fiz. 129(3), 464–490 (2001) [Theoret. and Math. Phys. 129 (3), 1694–1716 (2001)].

V. P. Maslov, Operator Methods (Nauka, Moscow, 1973) [in Russian].

D. S. Golikov and V. P. Maslov, “On the exact solution of the four-row matrix corresponding to the variational equations for ultrasecond quantization problems,” Mat. Zametki 83(2), 305–309 (2008) [Math. Notes 83 (2), 274–278 (2008)].

V. P. Maslov, “Revision of probability theory from the point of view of quantum statistics,” Russian J. Math. Phys., 14(1), 66–95 (2007).

H. Liu, J. He, J. Tang, et al., “Translocation of single-stranded DNA through single-walled carbon nanotubes,” Science 327(64), 64–67 (2010).

Ch. Y. Lee, W. Choi, J.-H. Han, and M. Strano, “Coherence resonance in a single-walled carbon nanotube ion channel,” Science 329(10) 1320–1324 (2010).

W. Choi, Z.W. Ulissi, S. Shimizu, et al., “Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotube,” Nature Communications (2013) (accepted 5 Aug 2013) (in press).