Solitons in fluctuating hydrodynamics of diffusive processes

Abstract

We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the Symmetric Exclusion Process (SEP). We show that the two fluid systems are related by a nonlinear transformation, which reveals an additional symmetry in the SEP system, but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, while sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.

Version to appear in PRE. An introduction reviewing the emergence of hydrodynamic equations in macroscopic fluctuation theory is added, and an additional symmetry in the SEP system is identified. 23 pages, 4 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Large Deviations in Single File Diffusion
• Special invited paper. Large deviations
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting