We review how the familiar notion of a thermodynamic potential can be generalized for a wide class of dynamical systems continuous in time and perturbed by weak noise; how, at least in principle, the description by means of nonequilibrium potentials can be reduced to discrete maps; and we present examples of nonequilibrium potentials for the one-dimensional logistic map. The latter result is used to calculate the critical exponent for the scaling of localized noise at the period doubling bifurcation sequence observed in numerical experiments by Mayer-Kress and Haken.
We dedicate this paper to Hermann Haken on the occasion of his 65th birthday.
KeywordsDiscrete Time System Period Doubling Total Entropy Noise Strength Continuous Time System
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