Repository: Freie Universit├Ąt Berlin, Math Department

Time scales and exponential trends to equilibrium: Gaussian model problems

Neureither, L. and Hartmann, C. (2019) Time scales and exponential trends to equilibrium: Gaussian model problems. In: Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, 282 . Springer, pp. 391-410. ISBN 978-3-030-15095-2


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We review results on the exponential convergence of multi- dimensional Ornstein-Uhlenbeck processes and discuss related notions of characteristic timescales with concrete model systems. We focus, on the one hand, on exit time distributions and provide ecplicit expressions for the exponential rate of the distribution in the small noise limit. On the other hand, we consider relaxation timescales of the process to its equi- librium measured in terms of relative entropy and discuss the connection with exit probabilities. Along these lines, we study examples which il- lustrate specific properties of the relaxation and discuss the possibility of deriving a simulation-based, empirical definition of slow and fast de- grees of freedom which builds upon a partitioning of the relative entropy functional in conjuction with the observed relaxation behaviour.

Item Type:Book Section
Additional Information:SFB 1114 Preprint: 02/2018 (authors version)
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2223
Deposited By: Silvia Hoemke
Deposited On:16 Feb 2018 16:02
Last Modified:16 Jan 2020 10:54

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