Entropic and gradient flow formulations for nonlinear diffusion

Nicolas Dirr, Marios Stamatakis, Johannes Zimmer

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4 Citations (Scopus)
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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.

Original languageEnglish
Article number081505
JournalJournal of Mathematical Physics
Volume57
Issue number8
DOIs
Publication statusPublished - 1 Aug 2016

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Gradient Flow
Nonlinear Diffusion
Thermodynamics
Zero-range Process
formulations
gradients
thermodynamics
Formulation
Metric
hydrodynamics
Fluctuating Hydrodynamics
Hydrodynamic Limit
Large Deviation Principle
Lyapunov Functional
Increment
nonlinearity
Entropy
Nonlinearity
entropy
deviation

Cite this

Entropic and gradient flow formulations for nonlinear diffusion. / Dirr, Nicolas; Stamatakis, Marios; Zimmer, Johannes.

In: Journal of Mathematical Physics, Vol. 57, No. 8, 081505, 01.08.2016.

Research output: Contribution to journalArticle

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