Kashlev, Yu. A. The second law of thermodynamics for high-energy channeled particles. (English. Russian original) Zbl 1201.80002 Theor. Math. Phys. 162, No. 2, 230-237 (2010); translation from Teor. Mat. Fiz. 162, No. 2, 275-284 (2010). The number of kinetic equations which lie behind the proof of the second law of thermodynamics is rather limited in the microscopic theory. This paper proves that the second law of thermodynamics is satisfied for high-energy particles, which move in a crystal in the channeling regime. This explicit proof involves a local Boltzmann equation for the distribution function of the particles written in the Bogoliubov form. Here, one statistical mechanism is taken into account, namely the scattering of channeled particles on lattice atoms randomly dislocated from the crystal sites. Reviewer: Viktor Shevchuk (Lviv) MSC: 80A05 Foundations of thermodynamics and heat transfer Keywords:thermodynamics; second law; channeled particle; crystal; Boltzmann kinetic equation; thermal scattering; distribution function; entropy; entropy source; local entropy balance equation PDF BibTeX XML Cite \textit{Yu. A. Kashlev}, Theor. Math. Phys. 162, No. 2, 230--237 (2010; Zbl 1201.80002); translation from Teor. Mat. Fiz. 162, No. 2, 275--284 (2010) Full Text: DOI References: [1] N. N. Bogoliubov, Problems of Dynamic Theory in Statistical Physics [in Russian], GITGL, Moscow (1946); English transl., Technical Inform. Serv., Oak Ridge, Tenn. (1960). [2] P. P. Kulik, ”Elastic interactions and transition phenomena,” in: Outline of the Physics and Chemistry of Low-Temperature Plasma (L. S. Polak, ed.), Nauka, Moscow (1971), pp. 5–55. [3] Yu. A. Kashlev and N. M. Sadykov, Phys. Stat. Sol. (b), 197, 19–29 (1996). · doi:10.1002/pssb.2221970105 [4] J. Lindhard, Mat.-Fys. Medd. Dan. Vid. Selsk, 34, No. 14, 3–63 (1965). [5] D. S. Gemmell, Rev. Modern Phys., 46, 129–227 (1974). · doi:10.1103/RevModPhys.46.129 [6] M. T. Robinson, Phys. Rev., 179, 327–342 (1969). · doi:10.1103/PhysRev.179.327 [7] E. Moreau and J. Salmon, J. Phys. Radium, 21, 217–222 (1960). · Zbl 0089.22402 · doi:10.1051/jphysrad:01960002104021700 [8] R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975). · Zbl 0984.82500 [9] P. Kubo, Thermodynamics, North-Holland, Amsterdam (1968). [10] Yu. A. Kashlev, Theor. Math. Phys., 140, 965–976 (2004). · doi:10.1023/B:TAMP.0000033033.66770.91 [11] T. Oshiyama, H. Kudo, and M. Mannami, J. Phys. Soc. Japan, 36, 1107–1113 (1974). · doi:10.1143/JPSJ.36.1107 [12] J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes, Springer, New York (1987). [13] M. S. Green, J. Chem. Phys., 20, 1281–1295 (1952). · doi:10.1063/1.1700722 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.