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  Interlacing relaxation and first-passage phenomena in reversible discrete and continuous space Markovian dynamics.

Hartich, D., & Godec, A. (2019). Interlacing relaxation and first-passage phenomena in reversible discrete and continuous space Markovian dynamics. Journal of Statistical Mechanics: Theory and Experiment, 2019: 024002. doi:10.1088/1742-5468/ab00df.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0003-1632-C Version Permalink: http://hdl.handle.net/21.11116/0000-0003-4E26-C
Genre: Journal Article

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 Creators:
Hartich, D.1, Author              
Godec, A.1, Author              
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1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              

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 Abstract: We uncover a duality between relaxation and first passage processes in ergodic reversible Markovian dynamics in both discrete and continuous state-space. The duality exists in the form of a spectral interlacing -- the respective time scales of relaxation and first passage are shown to interlace. Our canonical theory allows for the first time to determine the full first passage time distribution analytically from the simpler relaxation eigenspectrum. The duality is derived and proven rigorously for both discrete state Markov processes in arbitrary dimension and effectively one-dimensional diffusion processes, whereas we also discuss extensions to more complex scenarios. We apply our theory to a simple discrete-state protein folding model and to the Ornstein-Uhlenbeck process, for which we obtain the exact first passage time distribution analytically in terms of a Newton series of determinants of almost triangular matrices.

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Language(s): eng - English
 Dates: 2019-02-25
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1742-5468/ab00df
arXiv: 1802.10049
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Title: Journal of Statistical Mechanics: Theory and Experiment
Source Genre: Journal
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Pages: 28 Volume / Issue: 2019 Sequence Number: 024002 Start / End Page: - Identifier: -