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Uniqueness of thermodynamic projector and kinetic basis of molecular individualism

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  • Gorban, Alexander N.
  • Karlin, Iliya V.

Abstract

Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any vector field equipped with the given Lyapunov function into a vector field with the same Lyapunov function for a given anzatz manifold which is not tangent to the Lyapunov function levels.

Suggested Citation

  • Gorban, Alexander N. & Karlin, Iliya V., 2004. "Uniqueness of thermodynamic projector and kinetic basis of molecular individualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 391-432.
    • Handle: RePEc:eee:phsmap:v:336:y:2004:i:3:p:391-432
    DOI: 10.1016/j.physa.2004.01.039
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    References listed on IDEAS

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    1. Gorban, A.N & Karlin, I.V & Zmievskii, V.B & Dymova, S.V, 2000. "Reduced description in the reaction kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(3), pages 361-379.
    2. Gorban, Alexander N. & Karlin, Iliya V. & Zinovyev, Andrei Yu., 2004. "Invariant grids for reaction kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 106-154.
    3. Gorban, Alexander N. & Karlin, Iliya V., 1994. "General approach to constructing models of the Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 401-420.
    4. Grmela, Miroslav, 2002. "Reciprocity relations in thermodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 304-328.
    5. Gorban, Alexander N. & Karlin, Iliya V. & Zmievskii, Vladimir B. & Nonnenmacher, T.F., 1996. "Relaxational trajectories: global approximations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 648-672.
    6. Karlin, Iliya V. & Tatarinova, Larisa L. & Gorban, Alexander N. & Öttinger, Hans Christian, 2003. "Irreversibility in the short memory approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 399-424.
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    Cited by:

    1. Gorban, Alexander N. & Karlin, Iliya V., 2006. "Quasi-equilibrium closure hierarchies for the Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 325-364.

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