Entropic and gradient flow formulations for nonlinear diffusion

Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Stamatakis, Marios and Zimmer, Johannes 2016. Entropic and gradient flow formulations for nonlinear diffusion. Journal of Mathematical Physics 57 , 081505. 10.1063/1.4960748

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Abstract

Nonlinear diffusion is considered for a class of nonlinearities. It is shown that for some nonlinearities 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Entropy . Diffusion . Hydrodynamics . Boltzmann equations . Vector fields
Publisher:	American Institute of Physics
ISSN:	0022-2488
Funders:	EPSRC, Leverhulme Trust
Date of First Compliant Deposit:	10 October 2019
Date of Acceptance:	27 July 2016
Last Modified:	18 Nov 2024 00:30
URI:	https://orca.cardiff.ac.uk/id/eprint/94971

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