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The H-theorem for the physico-chemical kinetic equations with explicit time discretization

Author

Listed:
  • Adzhiev, S.Z.
  • Melikhov, I.V.
  • Vedenyapin, V.V.

Abstract

There is demonstrated in the present paper, that the H-theorem in the case of explicit time discretization of the physico-chemical kinetic equations, generally speaking, is not valid. We prove the H-theorem, when the system of the physico-chemical kinetic equations with explicit time discretization has the form of non-linear analogue of the Markov process with doubly stochastic matrix, and for more general cases. In these cases the proof is reduced to the proof of the H-theorem for Markov chains. The simplest discrete velocity models of the Boltzmann equation with explicit time discretization –the Carleman and Broadwell models are discussed and the H-theorem for them in the case of discrete time is proved.

Suggested Citation

  • Adzhiev, S.Z. & Melikhov, I.V. & Vedenyapin, V.V., 2017. "The H-theorem for the physico-chemical kinetic equations with explicit time discretization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 60-69.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:60-69
    DOI: 10.1016/j.physa.2017.03.032
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    Cited by:

    1. Adzhiev, S.Z. & Melikhov, I.V. & Vedenyapin, V.V., 2020. "On the H-theorem for the Becker–Döring system of equations for the cases of continuum approximation and discrete time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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