Work

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

Year: 2018

Type: article

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.

Source: New Journal of Physics

DOI: 10.1088/1367-2630/aaf038

Authors: David Hartich, Aljaž Godec

Institution: Max Planck Institute for Biophysical Chemistry

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,610

Funder: Deutsche Forschungsgemeinschaft