Oberseminar Mathematical Fluid Dynamics

We consider stochastic many-particle systems whose large-scale dynamics is described by a hyperbolic conservation
law for the particle density. While the typical behaviour of the particle system is given by entropy
solutions of the conservation law, large fluctuations are realized by non-entropic solutions such as travelling
wave profiles. Their probabilities are related to the corresponding entropy production, which has been made
rigorous for the totally asymmetric simple exclusion process by Jensen and Varadhan, and more recently by
Quastel and Tsai. We discuss this approach and some heuristic generalizations in the context of fluctuations of
the empirical current.
This is joint work with Paul Chleboun (Warwick, UK) and Andrea Pizzoferrato (Bath, UK).