| Abstract: |
| Fluctuations are ubiquitous in non-equilibrium conservative systems. The analysis of their large deviations lead to macroscopic fluctuation theory (MFT), a general framework for non-equilibrium statistical mechanics. MFT is based on a constitutive formula for large fluctuations around thermodynamic variables, and can be justified from fluctuating hydrodynamics. The latter postulates conservative, singular SPDEs to describe fluctuations in systems out of equilibrium. Both theories are informally linked via zero noise large deviations principles for SPDEs. In this talk, we will introduce several examples demonstrating these relations, and leading to a class of conservative SPDEs. The analysis of large deviations of interacting particle systems and conservative SPDEs will then lead to intricate and open problems for PDEs with irregular coefficients. In the last part of the talk, we present one positive result in this direction, solving a long-standing open problem in the proof of a full large deviation result for the zero-range process. |
|