Open Systems & Information Dynamics

, Volume 1, Issue 2, pp 149–182 | Cite as

Variational and extremum properties of homogeneous chemical kinetics. I. Lagrangian- and Hamiltonian-like formulations

  • S. Sieniutycz
  • J. S. Shiner


In this work we have constructed and compared various action-based variational approaches leading to nonstationary chemical kinetics and its asymptotic steady limit, Guldberg-Waage kinetics. We have shown that Guldberg-Waage kinetics is consistent with the chemical Lagrangian, eq. (14), at the steady state, but that it should be modified by an additional term (with the time derivative of the reaction rate) for very fast transients of the frequency greater than the ratio of the mean molecular velocity to the mean free path. These approaches developed here are consistent with the dissipative Lagrangian equations (with a Rayleigh dissipation function) and the Onsager-Machlup and Casimir formulations. The new action approach with the action explicit in the Lagrangian proposed here provides for the conservation of an energy-like integral which was missing in earlier approaches. At the same time it preserves a dissipation inequality by proving that an extended free energy, allowing for a dependence on the reaction rates, decreases in time.


Steady State Free Energy System Theory Free Path Time Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Nicholas Copernicus University Press 1992

Authors and Affiliations

  • S. Sieniutycz
    • 1
  • J. S. Shiner
    • 1
  1. 1.Physiologisches InstitutUniversität BernBernSwitzerland

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