The theory of multiplicative stochastic processes is contrasted with the theory of additive stochastic processes. The case of multiplicative factors which are purely random, Gaussian, stochastic processes is treated in detail. In a spirit originally introduced by theoretical work in nuclear magnetic resonance and greatly extended by Kubo, dissipative behavior is demonstrated, on the average, for dynamical equations which do not show dissipative behavior without averaging. It is suggested that multiplicative stochastic processes lead to a conceptual foundation for nonequilibrium thermodynamics and nonequilibrium statistical mechanics, of marked generality.
REFERENCES
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5.
L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959), Chap. 17.
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A. Redfield, Advances in Magnetic Resonance (Academic, New York, 1965), Vol. 1, pp. 1–32.
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R. Kubo, Fluctuations, Relaxation and Resonance in Magnetic Systems (Oliver and Boyd, Edinburgh, 1962), pp. 23–68.
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R. Kubo, “Stochastic Processes and Statistical Mechanics of Irreversible Processes,” Unpublished lecture notes (1963).
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See Ref. 10, note III of the Appendix.
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A. Einstein, Investigations on the Theory of the Brownian Movement (Dover, New York, 1956).
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See Ref. 10, Sec. 8.
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K. Huang, Statistical Mechanics (Wiley, New York, 1963), p. 203.
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© 1972 The American Institute of Physics.
1972
The American Institute of Physics
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