Open Systems & Information Dynamics

, Volume 2, Issue 1, pp 77–94 | Cite as

The statistical dynamics of activity-led reactions

  • S. Koseki
  • R. F. Streater


For any chemical reaction we construct a non-linear stochastic process in continuous or discrete time in which the concentrations obey a kinetic law, where the rates are proportional to the products of the activities. The main microscopic assumption can be interpreted as expressing the hypothesis of a collective effect related to saturation. The theory is unable to shed light on the problem of absolute rates. In the final section we suggest how the hypotheses of the model might be tested experimentally.


Statistical Physic Mechanical Engineer Stochastic Process System Theory Discrete Time 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. F. Streater, The Boltzmann Equation for Discrete System, inStatistical Mechanics, A. Solomon, ed., World Scientific, Singapore, 1988, pp. 101–132.Google Scholar
  2. [1a]
    L. Rondoni and R. F. Streater, J. Stat. Phys.66, 1557–1574, 1992.Google Scholar
  3. [1b]
    R. S. Ingarden and A. Kossakowski, Rep. Math. Phys.24, 177–186, 1986.Google Scholar
  4. [2]
    G. Kiegerl and F. Schürrer, Phys. Lett. A148, 158–163, 1990.Google Scholar
  5. [3]
    G. Kiegerl, Trans. Roy. Soc.: Phys. Sci. and Eng.342, 413–438 (1993).Google Scholar
  6. [4]
    R. K. Boyd, Chem. Rev.77, 93, 1977.Google Scholar
  7. [5]
    H. Eyring, S. H. Lin and S. M. Lin,Basic Chemical Kinetics, Wiley, New York, 1980, p. 405.Google Scholar
  8. [5a]
    J. Keizer:Statistical Thermodynamics of Non-equilibrium Processes, Springer, New York, 1987.Google Scholar
  9. [6]
    J. Keizer, loc. cit. p. 107.Google Scholar
  10. [7]
    R. F. Streater, Annals of Physics218, 255–278, 1992.Google Scholar
  11. [8]
    R. F. Streater, Statistical Dynamics, to appear in Rep. Math. Phys.Google Scholar
  12. [9]
    K. J. Laidler,Chemical Kinetics, 2nd Ed., McGraw Hill, London, 1965, p. 202.Google Scholar
  13. [10]
    R. F. Streater, Transport Theory and Statistical Physics22, 1–37, 1993.Google Scholar
  14. [11]
    R. H. Fowler,Statistical Mechanics, 2nd Ed., Cambridge, 1936, p. 703.Google Scholar
  15. [12]
    D. Godoris, A. Verbeure and P. Vets, J. Stat. Phys.56, 721–746, 1989.Google Scholar
  16. [13]
    S. Koseki, Ph.D. Thesis, King's College London, 1993.Google Scholar
  17. [14]
    R. F. Streater, J. Phys. A20, 4321, 1987.Google Scholar
  18. [15]
    A. B. Hope,Ion Transport and Membranes, Butterworths, London, 1971.Google Scholar
  19. [15a]
    O. Kedem and A. Essig, J. Gen. Physiol.48, 1047, 1965.Google Scholar
  20. [15b]
    G. E. Francis, W. Mulligan and A. Wormall,Isotopic Tracers, 2nd Ed., University of London, 1959, p. 345.Google Scholar

Copyright information

© Nicholas Copernicus University Press 1993

Authors and Affiliations

  • S. Koseki
    • 1
  • R. F. Streater
    • 1
  1. 1.Department of MathematicsKing's College London StrandLondonU.K.

Personalised recommendations