Dynamical Instability and Transport Coefficient in Deterministic Diffusion

Details Dynamical Instability and Transport Coefficient in Deterministic Diffusion Dynamical Instability and Transport Coefficient in Deterministic Diffusion

2011-09-26

arxiv.org/abs/1109.5464v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

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.

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