On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion

A. Mielke, D.R.M. Renger, M.A. Peletier

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43 Citaten (Scopus)
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Samenvatting

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions L that induce a flow, given by L(¿t,¿¿t)=0. We derive necessary and sufficient conditions for the unique existence of a generalized gradient structure for the induced flow, as well as explicit formulas for the corresponding driving entropy and dissipation functional. In particular, we show how these conditions can be given a probabilistic interpretation when L is associated to the large deviations of a microscopic particle system. Finally, we illustrate the theory for independent Brownian particles with drift, which leads to the entropy-Wasserstein gradient structure, and for independent Markovian particles on a finite state space, which leads to a previously unknown gradient structure. Keywords: Generalized gradient flows · Large deviations · Convex analysis · Particle systems
Originele taal-2Engels
Pagina's (van-tot)1293-1327
Aantal pagina's35
TijdschriftPotential Analysis
Volume41
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 2014

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