Entropic and gradient flow formulations for nonlinear diffusion

Nicolas Dirr, Marios Stamatakis, Johannes Zimmer

Research output: Contribution to journalArticlepeer-review

15 Citations (SciVal)
320 Downloads (Pure)


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
Issue number8
Publication statusPublished - 1 Aug 2016


Dive into the research topics of 'Entropic and gradient flow formulations for nonlinear diffusion'. Together they form a unique fingerprint.

Cite this