Cusp singularities in boundary-driven diffusive systems

Abstract

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities.\ The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.

References in corpus (3)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Non differentiable large-deviation functionals in boundary-driven diffusive systems

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