Extending transition path theory: periodically driven and finite-time dynamics
type: Item
instance of: scholarly article
title: Extending transition path theory: periodically driven and finite-time dynamics
zbMATH Open document ID: 1475.82013
author: Luzie Helfmann
author: Enric Ribera Borrell
author: Christof Schütte
author: Péter Koltai
published in: Journal of Nonlinear Science
publication date: 2021-04-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/2002.07474
review text: Given two distinct subsets \(A\), \(B\) in the state space of some dynamical system, transition path theory (TPT) was successfully used to describe the statistical behavior of transitions from \(A\) to \(B\) in the ergodic limit of the stationary system. In the present paper, generalizations of TPT are derived, that remove the requirements of stationarity and of the ergodic limit. This provides the tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. (We point out that originally TPT stems form molecular dynamics). The analysis is restricted to Markov processes on discrete state spaces, running in discrete time. The authors focus on the applicability of the general theory, e.g., nonequilibrium molecular, climate, fluid, or social dynamics (agent-based models). On simple model examples, mostly with numerical support, it is shown how the new tools deliver quantitative understanding about the statistical behavior of such systems. Five numerical examples, which refer to Markov chains on a finite-time interval, are discussed in separate subsections of Section 5. Section 6 is devoted to four numerical examples in the triple well landscape. These refer to several scenarios: infinite-time, stationary dynamics, that with an added periodic forcing, and finite-time dynamics. Technical proofs are relegated to appendices.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82C05
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 60J22
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 7341386
zbMATH Keywords: transition path theory (TPT)
zbMATH Keywords: Markov chains
zbMATH Keywords: time-inhomogeneous process
zbMATH Keywords: periodic driving
zbMATH Keywords: finite-time dynamics
zbMATH Keywords: infinite-time system
zbMATH Keywords: basins of attraction
zbMATH Keywords: commitor functions and equations
zbMATH Keywords: social and climate systems
zbMATH Keywords: human agent
zbMATH Keywords: numerical examples (Github package)
MaRDI profile type: Publication
OpenAlex ID: W3005982217
Wikidata QID: Q113063966
arXiv ID: 2002.07474
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DOI: 10.1007/S00332-020-09652-7
description: scientific article