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Large deviations and gradient flows
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Adams, S. (Stefan), Dirr, Nicolas, Peletier, M. A. (Mark A.) and Zimmer, Johannes (2013) Large deviations and gradient flows. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volulme 371 (Number 2002). Article Number 20120341. doi:10.1098/rsta.2012.0341 ISSN 1364-503X.
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Official URL: http://dx.doi.org/10.1098/rsta.2012.0341
Abstract
In recent work [1] we uncovered intriguing connections between Otto’s characterisation
of diffusion as entropic gradient flow [16] on one hand and large-deviation principles
describing the microscopic picture (Brownian motion) on the other. In this paper, we
sketch this connection, show how it generalises to a wider class of systems, and comment
on consequences and implications.
Specifically, we connect macroscopic gradient flows with large deviation principles,
and point out the potential of a bigger picture emerging: we indicate that in some nonequilibrium
situations, entropies and thermodynamic free energies can be derived via
large deviation principles. The approach advocated here is different from the established
hydrodynamic limit passage but extends a link that is well known in the equilibrium
situation.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||
Publisher: | The Royal Society Publishing | ||||
ISSN: | 1364-503X | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volulme 371 | ||||
Number: | Number 2002 | ||||
Article Number: | Article Number 20120341 | ||||
DOI: | 10.1098/rsta.2012.0341 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
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