Geometrical Interpretation of Fluctuating Hydrodynamics in Diffusive Systems

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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

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