Khinchin theorem and anomalous diffusion

Abstract

A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York) 1949] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a Generalized Langevin Equation the Khinchin theorem holds.

4 pages, 3 figures

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• Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
• Violation of the fluctuation-dissipation theorem for fast superdiffusion
• Intermediate dynamics between Newton and Langevin
• Non-exponential relaxation for anomalous diffusion
• Two time scales and FDT violation in a Finite Dimensional Model for Structural Glasses
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• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Superdiffusion in self-reinforcing run-and-tumble model with rests
• Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
• Phase Transitions in Ehrenfest Urns Model with Interactions: Coexistence of uniform and non-uniform states
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• Fractality in resistive circuits: The Fibonacci resistor networks
• Nonergodic Brownian oscillator: High-frequency response
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model
• Generalized Khinchin Theorem for a Class of Aging Processes