Density large deviations for multidimensional stochastic hyperbolic conservation laws

Abstract

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the conductivity and dif-fusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in [4]. When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a general weak solution, and leave the general large deviation function upper bound as a conjecture.

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• Sampling rare events across dynamical phase transitions
• Gamma Convergence Approach For The Large Deviations Of The Density In Systems Of Interacting Diffusion Processes
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps