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Duality between relaxation and first passage in reversible Markov dynamics: Rugged energy landscapes disentangled.

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Hartich,  D.
Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

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Godec,  A.
Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

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Citation

Hartich, D., & Godec, A. (2018). Duality between relaxation and first passage in reversible Markov dynamics: Rugged energy landscapes disentangled. New Journal of Physics, 20(11): 112002. doi:10.1088/1367-2630/aaf038.


Cite as: http://hdl.handle.net/21.11116/0000-0002-9280-7
Abstract
Relaxation and first passage processes are the pillars of kinetics in condensed matter, polymeric and single-molecule systems. Yet, an explicit connection between relaxation and first passage time-scales so far remained elusive. Here we prove a duality between them in the form of an interlacing of spectra. In the basic form the duality holds for reversible Markov processes to effectively one-dimensional targets. The exploration of a triple-well potential is analyzed to demonstrate how the duality allows for an intuitive understanding of first passage trajectories in terms of relaxational eigenmodes. More generally, we provide a comprehensive explanation of the full statistics of reactive trajectories in rugged potentials, incl. the so-called 'few-encounter limit'. Our results are required for explaining quantitatively the occurrence of diseases triggered by protein misfolding.