Theory of nonequilibrium transport based on a class of chaotic fluctuations

We present a mathematical theory on the transport of mesoscopic particle under the action of a class of nonequilibrium chaotic fluctuations. By considering a perturbative Perron-Frobenius approach on a strongly damped particle in a potential field, we arrive at a transport equation in the form of an inhomogeneous Smoluchowski equation with a source term. The source term is identified to be associated with the statistical asymmetry of the chaotic fluctuations. In particular, the theory has enabled us to give a quantitative account for various nonequilibrium phenomena, such as: the directed current, the desymmetrization of particle distributions, the enhancement or suppression of Kramers escape rate, as well as the correspondence between chaotic and stochastic resonance. Moreover, under the condition of free field, we have found interesting connection between the particle dynamics and statistical mechanics, and have uncovered the surprising result that a non-Ornstein-Uhlenbeck deterministic process can generate a stochastic Gaussian diffusion process.

Author dc:creator

• CHEW LOCK YUE

• Chaotic transport, Nonequilibrium fluctuations, Brownian ratchet, Gaussian diffusion process, Kramers problem, Chaotic resonance.