Abstract
A method for classifying the states of a macroscopic dissipative system according to their stability with respect to finite-amplitude localized fluctuations and perturbations is presented. Since the method does not rely on a extremum principle it is applicable to open systems far from equilibrium. It appears that in general there exists at most one absolutely stable state (up to symmetry). Simple examples are given for systems without absolutely stable state.
Similar content being viewed by others
References
Eckern, U., Schmid, A., Schmutz, M., Schön, G.: J. Low Temp. Phys.36, 643 (1979)
Graham, R., Haken, H.: Z. Phys. A — Atoms and Nuclei243, 289 (1971);245, 141 (1971)
Kampen, N.G. van: Phys. Rev. A135, 362 (1964)
Langer, J.S.: Ann. Phys. (N.Y.)41, 108 (1967)
Haken, H.: Rev. Mod. Phys.47, 67 (1975)
Nicolis, G., Prigogine, I.: Self-Organization in Nonequilibrium Systems, John Wiley, 1977; Haken, H.: Synergetics. Berlin, Heidelberg, New York: Springer 1978
Schlögl, F.: Phys. Rep.62, 268 (1980)
See e.g. May, R.M.: Stability and Complexity in Model Ecosystems. Princeton: Princeton University Press 1974
Suzuki, M.: Prog. Theor. Phys. (Kyoto)53, 1657 (1975)
Görtz, R.: Physica90A, 360 (1978); Z. Phys. B — Condensed Matter36, 373 (1980)
Graham, R., to appear in: Stochastic Nonlinear Systems in Physics, Chemistry, and Biology, Arnold, L., Lefever, R. (eds.). Berlin, Heidelberg, New York: Springer 1981
Likharev, K.K.: Pis'ma Zh. Eksp. Teor. Fiz.20, 730 (1974); JETP Lett.20, 338 (1974)
Kramer, L., Baratoff, A.: Phys. Rev. Lett.38, 518 (1977);
Kramer, L., Watts-Tobin, R.J.: Phys. Rev. Lett.40, 1041 (1978); Watts-Tobin, R.J., Krähenbühl, I., Kramer, L.: J. Low Temp. Phys. (to appear)
Coleman, S.: Phys. Rev. D15, 2929 (1977); D16, 1248(E) (1977); Callan, C., Coleman, S.: Phys. Rev. D16, 1762 (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kramer, L. On the relative stability of states and first-order phase transition in systems far from equilibrium. Z. Physik B - Condensed Matter 41, 357–363 (1981). https://doi.org/10.1007/BF01307327
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01307327