Entropic and gradient flow formulations for nonlinear diffusion

Nicolas Dirr, Marios Stamatakis, Johannes Zimmer

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

15 Zitate (Scopus)

Abstract

Nonlinear diffusion ∂tρ= (increment)(Φ(ρ)) is considered for a class of nonlinearities Φ. It is shown that for suitable choices of Φ, an associated Lyapunov functional can be interpreted as thermodynamic entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role.

OriginalspracheEnglisch
Aufsatznummer081505
FachzeitschriftJournal of Mathematical Physics
Jahrgang57
Ausgabenummer8
DOIs
PublikationsstatusVeröffentlicht - 1 Aug. 2016
Extern publiziertJa

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