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Thermodynamics and tropical mathematics. Definition of quasistatistical processes. (English) Zbl 1342.82057
Summary: We consider the relations between thermodynamics on the one hand and the $$(\max,+)$$-algebra and tropical mathematics on the other hand. The contribution of Grigorii Litvinov to tropical geometry is emphasized. Relations for a liquid in the negative pressure domain are given.

##### MSC:
 82B30 Statistical thermodynamics 82D15 Statistical mechanics of liquids
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##### References:
 [1] V. N. Kolokoltsov and V. P. Maslov, Idempotent Analysis and Its Applications (Kluwer, Dordrecht-Boston-London, 1997). · Zbl 0941.93001 [2] G. L. Litvinov, “Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry,” arXiv:1005.1247v1 [math-ph]. · Zbl 1223.14070 [3] Simon, I., Recognizable sets with multiplicities in the tropical semiring, Lect. Notes Comput. Sci., 324, 107-120, (1988) · Zbl 0656.68086 [4] Viro, O., Dequantization of real algebraic geometry on logarithmic paper, European Congress of Mathematics, I, 135-146, (2001) · Zbl 1024.14026 [5] Maslov, V. P., Case of less than two degrees of freedom, negative pressure, and the Fermi-Dirac distribution for a hard liquid, Math. Notes, 98, 138-157, (2015) · Zbl 1329.82128 [6] Maslov, V. P., Mathematical conception of “phenomenological” equilibrium thermodynamics, Russ. J.^Math. Phys., 18, 363-370, (2011) · Zbl 1326.82009 [7] Maslov, V. P., Undistinguishing statistics of objectively distinguishable objects: thermodynamics and superfluidity of classical gas, Math. Notes, 94, 722-813, (2013) · Zbl 1290.82032 [8] Maslov, V. P., New construction of classical thermodynamics and UD-statistics, Russian J. Math. Phys., 21, 256-284, (2014) · Zbl 1311.82019 [9] L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian]. · Zbl 0859.76001 [10] 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]. [11] Maslov, V. P., Solution of the Gibbs paradox in the framework of classical mechanics (statistical physics) and crystallization of the gas C_{60}, Mat. Zametki, 83, 787-791, (2008) · Zbl 1157.82003 [12] Dai, W.-S.; Xie, M., Gentile statistics with a large maximum occupation number, Annals of Physics, 309, 295-305, (2004) · Zbl 1037.81104 [13] Maslov, V. P., The relationship between the Van-der-Waals model and the undistinguishing statistics of objectively distinguishable objects. the new parastatistics, Russian J. Math. Phys., 21, 99-111, (2014) · Zbl 1311.81256 [14] Maslov, V. P., Statistics corresponding to classical thermodynamics. construction of isotherms, Russian J. Math. Phys., 22, 53-67, (2015) · Zbl 1320.82027 [15] Maslov, V.P., Gas-amorphous solid and liquid-amorphous solid phase transitions. introduction of negative mass and pressure from the mathematical viewpoint, Math. Notes, 97, 423-430, (2015) · Zbl 1320.82021 [16] Temperly, H. N., No article title, Proc. Phys. Soc. (L.), 59, 199-205, (1947) [17] Maslov, V.P., Generalization of tropical geometry and amebas to the region of negative pressures: comparison with van der Waals gas, Math. Notes, 98, 429-440, (2015) · Zbl 1341.82069
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