Dynamical Instability and Transport Coefficient in Deterministic Diffusion

Abstract

We construct both normal and anomalous deterministic biased diffusions to obtain the Einstein relation for their time-averaged transport coefficients. We find that the difference of the generalized Lyapunov exponent between biased and unbiased deterministic diffusions is related to the normalized velocity based on the ensemble average. By Hopf's ergodic theorem, the ratios between the time-averaged velocity and the Lyapunov exponent for single trajectories converge to a universal constant, which is proportional to the strength of the bias. We confirm this theory using numerical simulations.

5 pages, 3 figures

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• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• Pesin-Type Identity for Weak Chaos
• Nonergodisity of a time series obeying Lévy statistics
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Cited by in corpus (4)

• Distributional Response to Biases in Deterministic Superdiffusion
• A memory-induced diffusive-superdiffusive transition: ensemble and time-averaged observables
• Generalized Lyapunov exponent as a unified characterization of dynamical instabilities
• Inhomogeneous diffusion and ergodicity breaking induced by global memory effects