Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

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.Comment: 19 page

Amenable ergodic group actions and an application to Poisson boundaries of random walks

AbstractWe introduce and study the class of amenable ergodic group actions which occupy a position in ergodic theory parallel to that of amenable groups in group theory. We apply this notion to questions about skew products, the range (i.e., Poincaré flow) of a cocycle, and to Poisson boundaries