Skip to main content
SpringerLink
Log in

The second law of thermodynamics for high-energy channeled particles

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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).

    Google Scholar 

  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.

    Google Scholar 

  3. Yu. A. Kashlev and N. M. Sadykov, Phys. Stat. Sol. (b), 197, 19–29 (1996).

    Article  ADS  Google Scholar 

  4. J. Lindhard, Mat.-Fys. Medd. Dan. Vid. Selsk, 34, No. 14, 3–63 (1965).

    Google Scholar 

  5. D. S. Gemmell, Rev. Modern Phys., 46, 129–227 (1974).

    Article  ADS  Google Scholar 

  6. M. T. Robinson, Phys. Rev., 179, 327–342 (1969).

    Article  ADS  Google Scholar 

  7. E. Moreau and J. Salmon, J. Phys. Radium, 21, 217–222 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975).

    MATH  Google Scholar 

  9. P. Kubo, Thermodynamics, North-Holland, Amsterdam (1968).

    Google Scholar 

  10. Yu. A. Kashlev, Theor. Math. Phys., 140, 965–976 (2004).

    Article  Google Scholar 

  11. T. Oshiyama, H. Kudo, and M. Mannami, J. Phys. Soc. Japan, 36, 1107–1113 (1974).

    Article  ADS  Google Scholar 

  12. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes, Springer, New York (1987).

    Google Scholar 

  13. M. S. Green, J. Chem. Phys., 20, 1281–1295 (1952).

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Baikov Institute for Metallurgy and Material Science, RAS, Moscow, Russia

    Yu. A. Kashlev

Authors
  1. Yu. A. Kashlev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 162, No. 2, pp. 275–284, February, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kashlev, Y.A. The second law of thermodynamics for high-energy channeled particles. Theor Math Phys 162, 230–237 (2010). https://doi.org/10.1007/s11232-010-0018-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-010-0018-2

Keywords

Search

Navigation