Abstract
Macroscopic systems are frequently described in terms of a set of macroscopic variables staisfying a given system of deterministic differential equations. The fluctuations of macroscopic variables being small, such a deterministic description is, in many cases, sufficiently accurate and already contains a wealth of information: e.g., for systems which are driven by stationary external forces and interacting with time independent reservoirs, the deterministic description allows to discuss the steady state as a fixed point or a limit cycle or a more complicated ‘strange attractor’ in the space of the macroscopic variables. Within the same description it is also possible to discuss the stability of the various steady states, in which the system may be found, and the time dependent relaxation towards such states from a given initial state.
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References
M. Lax, Rev. Mod. Phys. 32: 25 (1960);
M. Lax, Rev. Mod. Phys. 38:359 (1966)
M. Lax, Rev. Mod. Phys. 38:541 (1966).
T. Kirkpatrick, E.G.D. Cohen, J.R. Dorfman, Phys. Rev. Lett. 44: 472 (1980).
I. Procaccia, D. Ronis, I. Oppenheim, Phys. Rev. A20: 2533 (1979).
H. Haken, Encyclopedia of Physics 25/2c, Springer, New York 1970.
R. Graham, Springer Tracts in Mod. Phys. 66, Springer, New York 1973.
H. Haken, Rev. Mod. Phys. 47: 67 (1975).
R. Graham, in “Order and Fluctuations in Equilibrium and Non-equilibrium Statistical Mechanics”, ed. Nicolis et al., John Wiley, New York (1981), p. 235.
’ E. N. Lorenz, J. Atmos. Sci. 20: 130 (1963).
D. Ruelle, F. Takens, Commun. Math. Phvs. 20: 167 (1971).
R.L. Stratonovich, “Topics in the Theory of Random Noise,” Vol. I, II, Gordon and Breach, New York 1963.
H. Risken, Z. Physik 251: 231 (1972).
R. Graham, Z. Physik B40: 149 (1980).
R. Graham, H. Haken Z. Physik 243: 289 (1971)
R. Graham, H. Haken Z. Physik 245:141 (1971).
R. Graham, in Coherence and Quantum Optics, ed. L. Mandel, E. Wolf, Plenum, New York 1973.
R. Graham, in “Fluctuations, Instabilities and Phase Transitions,” ed. T. Riste, Plenum, New York 1975.
H. Risken, H.D. Vollmer, Z. Physik 201: 323 (1967);
H. Risken, H.D. Vollmer, Z. Physik 204:240 (1967)
K. Seybold, H. Risken, Z. Physik 267: 323 (1974).
A. Schenzle, H. Brand, Phys. Rev. A4: 1628 (1979).
R. Graham, Phys. Lett. 80A: 351 (1980).
S.L. McCall, Phys. Rev. A9: 1515 (1974)
H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan, Phys. Rev. Lett. 36: 1135 (1976)
R. Graham, A. Schenzle, in “Proceedings of the International Optical Bistability Conference,” Asheville, N.C. USA, 1980; R. Graham, A. Schenzle, Phys. Rev. A23, to appear.
R. Graham, H.J. Scholz, Phys. Rev. A22: 1198 (1980).
L.D. Landau, E.M. Lifshitz, “Fluid Mechanics”, Pergamon, London 1958.
L.D. Landau, E.M. Lifshitz, “Statistical Physics”, Pergamon, London 1959.
S. Grossmann, J. Chem. Phys. 65: 2007 (1976).
C. Gardiner, J. Stat. Phys. 14: 309 (1976).
N. van Kampen, in “Topics in Statistical Mechanics and Biophysics,” ed. R. A. Piccirelli, 1976.
W. Horsthemke, L. Brenig, Z. Physik B27: 341 (1977).
S.R. DeGroot, P. Mazur, “Non equilibrium thermodynamics,” North Holland, Amsterdam 1962.
A. Schenzle, H. Brand, Optics Commun. 23: 151 (1978).
A. Schenzle, H. Brand, Optics Commun. 31: 401 (1979).
R. Graham, Phys. Rev. Lett. 31: 1479 (1973)
R. Graham, Phys. Rev. A10: 1762 (1974).
W.A. Smith, Phys. Rev. Lett. 32: 1164 (1974).
I.S. Gradsteyn, I.M. Ryshik, “Table of Integrals, Series and Products,” Academic, New York 1965.
M. Abramowitz, I. Stegun, “Handbook of Mathematical Functions,” Dover, New York 1965.
H. Haken, Phys. Lett. 53A: 77(1975).
R. Graham, Phys. Lett. 58A: 440 (1976).
K.A. Robbins, Proc. Natl. Acad. Sci. USA 73: 4297 (1976).
J.B. McLaughlin, P.C. Martin, Phys. Rev. A12: 186 (1975); O. Lanford in “Turbulence Seminar”, Lecture Notes in Mathematics 615: 113, Springer, New York 1977.
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Graham, R. (1981). Models of Stochastic Behavior in Non-Equilibrium Steady States. In: Chen, SH., Chu, B., Nossal, R. (eds) Scattering Techniques Applied to Supramolecular and Nonequilibrium Systems. NATO Advanced Study Institutes Series, vol 73. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4061-4_26
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DOI: https://doi.org/10.1007/978-1-4684-4061-4_26
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