Synergetics pp 69-103 | Cite as


How Far a Drunken Man Can Walk
  • Hermann Haken


While in Chapter 2 we dealt with a fixed probability measure, we now study stochastic processes in which the probability measure changes with time. We first treat models of Brownian movement as example for a completely stochastic motion. We then show how further and further constraints, for example in the frame of a master equation, render the stochastic process a more and more deterministic process.


Brownian Movement Conditional Probability Stationary Solution Markov Process Joint Probability 
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. N. Wax, ed.: Selected Papers on Noise and Statistical Processes (Dover Publ. Inc., New York 1954) with articles by S. Chandrasekhar, G. E. Uhlenbeck and L. S. Ornstein, Ming Chen Wang and G. E. Uhlenbeck, M. KacGoogle Scholar
  2. T. T. Soong: Random Differential Equations in Science and Engineering (Academic Press, New York 1973)zbMATHGoogle Scholar
  3. M. Kac: Am. Math. Month. 54, 295 (1946)Google Scholar
  4. M. S. Bartlett: Stochastic Processes (Univ. Press, Cambridge 1960)zbMATHGoogle Scholar
  5. R. L. Stratonovich: Topics in the Theory of Random Noise (Gordon Breach, New York-London, Vol. I 1963, Vol. II 1967)Google Scholar
  6. M. Lax: Rev. Mod. Phys. 32, 25 (1960); 38, 358 (1965); 38, 541 (1966)ADSzbMATHCrossRefGoogle Scholar
  7. H. Pauli: Probleme der Modernen Physik. Festschrift zum 60. Geburtstage A. Sommerfelds, ed. by P. Debye (Hirzel, Leipzig 1928)Google Scholar
  8. L. van Hove: Physica 23,441 (1957)MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. S. Nakajiama: Progr. Theor. Phys. 20, 948 (1958)ADSCrossRefGoogle Scholar
  10. R. Zwanzig: J. Chem. Phys. 33, 1338 (1960)MathSciNetADSCrossRefGoogle Scholar
  11. E. W. Montroll: Fundamental Problems in Statistical Mechanics, compiled by E. D. G. Cohen (North Holland, Amsterdam 1962)Google Scholar
  12. P. N. Argyres, P. L. Kelley: Phys. Rev. 134, A98 (1964)ADSCrossRefGoogle Scholar
  13. F. Haake: In Springer Tracts in Modern Physics, Vol. 66 (Springer, Berlin-Heidelberg-New York 1973) p. 98.Google Scholar
  14. H. Haken: Phys. Lett. 46A, 443 (1974); Rev. Mod. Phys. 47, 67 (1975)ADSGoogle Scholar
  15. R. Landauer: J. Appl. Phys. 33, 2209 (1962)ADSCrossRefGoogle Scholar
  16. G. Kirchhoff: Ann. Phys. Chem., Bd. LXXII 1847, Bd. 12, S. 32Google Scholar
  17. G. Kirchhoff: Poggendorifs Ann. Phys. 72, 495 (1844)Google Scholar
  18. R. Bott, J. P. Mayberry: Matrices and Trees, Economic Activity Analysis (Wiley, New York 1954)Google Scholar
  19. E. L. King, C. Altmann: J. Phys. Chem. 60, 1375 (1956)CrossRefGoogle Scholar
  20. T. L. Hill: J. Theor. Biol. 10,442 (1966)CrossRefGoogle Scholar
  21. W. Weidlich; Stuttgart (unpublished)Google Scholar
  22. I. Schnakenberg: Rev. Mod. Phys. 48, 571 (1976)MathSciNetADSCrossRefGoogle Scholar
  23. J. Keizer: On the Solutions and the Steady States of a Master Equation (Plenum Press, New York 1972)Google Scholar
  24. P. Ehrenfest and T. Ehrenfest: Phys. Z. 8, 311 (1907)Google Scholar
  25. A. Münster: In Encyclopedia of Physics, ed. by S. Flügge, Vol. III/2: Principles of Thermodynamics and Statistics (Springer, Berlin-Göttingen-Heidelberg 1959)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Germany

Personalised recommendations