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 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.

arXiv comment19 pages

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Cited by in corpus (10)

• On Dean-Kawasaki Dynamics with Smooth Drift Potential
• Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance
• Entropic and gradient flow formulations for nonlinear diffusion
• Computing diffusivities from particle models out of equilibrium
• Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory
• Stochastic dynamics of collective modes for Brownian dipoles
• Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics
• Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality
• Emergence of particle clusters in a one-dimensional model: connection to condensation processes
• Ill-posedness of the pure-noise Dean-Kawasaki equation