Stability in the dissipative steady state

NOV 01, 1978

Systems requiring a continuous inflow of energy to maintain their state exhibit many analogies to equilibrium but their behavior is more strongly influenced by noise.

DOI: 10.1063/1.2994813

Rolf Landauer

Stability questions arise in a number of different ways. At the simplest level we can ask about the stability of a particle in a force field. It is stable if any deviations of the particle from its initial location cause it to be exposed to forces returning it back to the initial point. With time, however, “stability” has taken on a broader meaning. We find references to the stability of an orbit, of a laser’s mode of oscillation, or of a set of biological populations. Harry L. Swinney and Jerry P. Gollub recently discussed the stability of liquid flow patterns in PHYSICS TODAY (August, page 41). In all of these cases there are questions about the persistence of an initial behavior pattern.

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References

1. Synergetics, A Workshop, (H. Haken, ed.) Springer, Heidelberg (1977).
2. Bifurcation Theory and its Applications in Scientific Disciplines (O. E. Rössler, O. Gurel, eds.) Ann. N.Y. Acad. Sci., to be published.
3. Fluctuations, Instabilities, and Phase Transitions (T. Riste, ed.) Plenum Publishing Corp., New York (1975).
4. Physical Chemistry of Oscillatory Phenomena, Faraday Society Conf. Proceedings, University Press, Aberdeen (1975).
5. Ber Bunsengesells, Phys. Chem. 80, 1041–1256 (1976).
6. I. Prigogine, Science 201, 777 (1978). https://doi.org/SCIEAS
For a critical assessment of the detailed results of Prigogine’s “Brussels” school, see B. H. Lavenda, Thermodynamics of Irreversible Processes, Wiley, New York (1978).
7. R. Thom, Stabilité Structured et Morphogénèse, W. A. Benjamin, Reading, Mass. (1972).
8. G. Kolata, Science 196, 287 (1977).https://doi.org/SCIEAS
9. H. Th. Simon, Phys. Z. 6, 297 (1905).https://doi.org/PHZTAO
10. H. Busch, Stabilität, Labilität und Pendelungen in der Elektrotechnik, S. Hirzel, Leipzig (1913).
11. R. A. Schmitz, in Chemical Reaction Engineering Reviews (H. M. Hulburt, ed.) Am. Chem. Soc., Washington, D.C. (1975) page 156;
R. Aris, in Bifurcation Theory and its Applications in Scientific Disciplines (O. E. Rössler, O. Gurel, eds.) Ann. N.Y. Acad. Sci., to be published.
12. J. von Neumann, U.S. Patent 2 815 488.
13. E. Goto, J. Electrical Commun. Eng. Jap. 38, 770 (1955).
14. A. M. Turing, Philos. Trans. R. Soc. Lond. B 237, 37 (1952).https://doi.org/PTRBAE
15. E. Goto, K. Murata, K. Nakazawa, K. Nakagawa, T. Motsoka, Y. Motsuoka, Y. Ishibashi, H. Ishida, T. Soma, E. Wade, IRE Trans. on Electronic Computers EC‐9, 25 (1960).https://doi.org/IRELAO
16. H. Busch, Ann. Phys. (Leipz.) 64, 401 (1921).https://doi.org/ANPYA2
17. B. Ross, J. D. Litster, Phys. Rev. A 15, 1246 (1977).https://doi.org/PLRAAN
18. W. J. Skocpol, M. R. Beasley, M. Tinkham, J. Appl. Phys. 45, 4054 (1974).https://doi.org/JAPIAU
19. R. Landauer, J. W. F. Woo, Comments on Solid State Phys. 4, 139 (1972).https://doi.org/COSPBK
20. R. L. Stratonovich, Topics in the Theory of Random Noise, Vols. I and II, Gordon and Breach, New York (1963) and (1967).
21. H. Haken, Rev. Mod. Phys. 47, 67 (1975); https://doi.org/RMPHAT
Synergetics, An Introduction, Springer, Heidelberg (1977).
22. N. G. van Kampen, Phys. Lett. A, 62, 383 (1977).https://doi.org/PYLAAG
23. C. W. Gardiner, S. Chaturdevi, D. F. Walls, in ref. 2.
24. For discussions of the origins of life, see contribution by H. Kuhn and by M. Eigen in ref. 5.
See also H. Kuhn, Phys. Bl. 34, 208 (1978); https://doi.org/PHBLAG
H. Kuhn, Phys. Bl. 34, 255 (1978).https://doi.org/PHBLAG

More about the Authors

Rolf Landauer. Thomas J. Watson Research Center of IBM, Yorktown Heights, N.Y..