Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

Robert L. Jack; Johannes Zimmer

doi:10.1088/1751-8113/47/48/485001

Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

Robert L. Jack, Johannes Zimmer

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Abstract

We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles - the Wasserstein geometry - which allows the deterministic hydrodynamic evolution of the systems to be related to the steepest descent of the free energy, and show how this formulation can be related to most probable paths of mesoscopic dissipative systems. The geometric viewpoint is also linked to fluctuating hydrodynamics of these systems via a saddle point argument.

Original language	English
Article number	485001
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	47
Issue number	48
DOIs	https://doi.org/10.1088/1751-8113/47/48/485001
Publication status	Published - 5 Dec 2014

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title = "Geometrical interpretation of fluctuating hydrodynamics in diffusive systems",

abstract = "We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles - the Wasserstein geometry - which allows the deterministic hydrodynamic evolution of the systems to be related to the steepest descent of the free energy, and show how this formulation can be related to most probable paths of mesoscopic dissipative systems. The geometric viewpoint is also linked to fluctuating hydrodynamics of these systems via a saddle point argument.",

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AB - We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles - the Wasserstein geometry - which allows the deterministic hydrodynamic evolution of the systems to be related to the steepest descent of the free energy, and show how this formulation can be related to most probable paths of mesoscopic dissipative systems. The geometric viewpoint is also linked to fluctuating hydrodynamics of these systems via a saddle point argument.

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Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

Abstract

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Analysis of the Effective Long Time-Behaviour of Molecule Systems

Fellowship - How Fast does Time Flow? Dynamic Behaviour in Glasses, Nano-Science and Self-Assembly

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Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

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Analysis of the Effective Long Time-Behaviour of Molecule Systems

Fellowship - How Fast does Time Flow? Dynamic Behaviour in Glasses, Nano-Science and Self-Assembly

Cite this