Geodesic
The second law of thermodynamics for high-energy channeled particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 275-284
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In microscopic theory, the number of kinetic equations underlying the proof of the second law of thermodynamics is quite restricted. We explicitly prove that the second law of thermodynamics is satisfied for high-energy particles moving in a crystal in the channeling regime. The proof involves a local Boltzmann equation for the distribution function of the particles written in the Bogoliubov form. In this, we take one statistical mechanism into account: the scattering of channeled particles on lattice atoms randomly displaced from the crystal sites.
Keywords: thermodynamics, second law, channeled particle, crystal, Boltzmann kinetic equation, thermal scattering, distribution function, entropy, entropy source, local entropy balance equation. 
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Yu. A. Kashlev. The second law of thermodynamics for high-energy channeled particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 275-284. http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a8/

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