Nonergodic solutions of the generalized Langevin equation.
TLDR
It is shown that the generalized Langevin equation may have nonergodic (nonstationary) solutions even if the integral of the memory function is finite and diffusion is normal.Abstract:
It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have nonergodic solutions that do not relax to equilibrium values. It is shown that the equation may have nonergodic (nonstationary) solutions even if the integral of the memory function is finite and diffusion is normal.read more
Citations
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Localized mode and nonergodicity of a harmonic oscillator chain
Fumihiro Ishikawa,Synge Todo +1 more
TL;DR: In this paper, a simple and microscopic physical model that breaks the ergodicity was presented, which consists of coupled classical harmonic oscillators, and the motion of the tagged particle obeys the generalized Langevin equation satisfying the second fluctuation dissipation theorem.
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Non-Markovian Two-Time Correlation Dynamics and Nonergodicity
TL;DR: In this paper, two-time correlation functions of the coordinate and velocity of a non-Markovian harmonic particle are derived analytically and decomposed into the components of differences between the initial variances and the equilibrium of the particle; in particular, the dependence of a random force on the initial preparation of the system is included.
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Stochastic dynamics beyond the weak coupling limit: thermalization.
TL;DR: Generalized fluctuation-dissipation relations are derived and shown to ensure convergence to thermal equilibrium to any order in λ.
Journal ArticleDOI
Generalized Einstein relations and conditions for anomalous relaxation.
TL;DR: The generalized Einstein relation (GER) for nonergodic processes is investigated within the framework of the generalized Langevin equation and it is shown that the GER holding is a necessary condition rather than a full condition for the system being close to equilibrium.
References
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Book
Nonequilibrium statistical mechanics
TL;DR: The paradoxes of irreversibility as mentioned in this paper is a well-known problem in nonlinear problems, and it has been studied extensively in the literature for a long time, e.g. in the context of projection operators.