# Cusp Singularities in Boundary-Driven Diffusive Systems

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## 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.

## Keywords

Boundary-driven diffusive systems Rare events Large deviations Phase-transitions Catastrophe theory## Notes

### Acknowledgements

We are grateful for discussions with B. Derrida, J. Kurchan, O. Raz and J. Tailleur. This research was funded by BSF and ISF grants, and by the European Union’s—Seventh Framework Programme (FP7/2007–2013) under grant agreement No. 276923—MC-MOTIPROX.

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