Cusp Singularities in Boundary-Driven Diffusive Systems
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- Bunin, G., Kafri, Y. & Podolsky, D. J Stat Phys (2013) 152: 112. doi:10.1007/s10955-013-0752-6
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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.