English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We uncover a duality between relaxation and first passage processes inergodic reversible Markovian dynamics in both discrete and continuousstate-space. The duality exists in the form of a spectral interlacing -- therespective time scales of relaxation and first passage are shown to interlace.Our canonical theory allows for the first time to determine the full firstpassage time distribution analytically from the simpler relaxationeigenspectrum. The duality is derived and proven rigorously for both discretestate Markov processes in arbitrary dimension and effectively one-dimensionaldiffusion processes, whereas we also discuss extensions to more complexscenarios. We apply our theory to a simple discrete-state protein folding modeland to the Ornstein-Uhlenbeck process, for which we obtain the exact firstpassage time distribution analytically in terms of a Newton series ofdeterminants of almost triangular matrices.

Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics