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Journal of Statistical Physics

, Volume 152, Issue 1, pp 112–135 | Cite as

Cusp Singularities in Boundary-Driven Diffusive Systems

  • Guy Bunin
  • Yariv Kafri
  • Daniel Podolsky
Article

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Technion—Israel Institute of TechnologyHaifaIsrael

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