A Few Exact Results on Non-Equilibrium Fluctuations

Understanding macroscopic fluctuations outside equilibrium is crucial for developing a potential theory of non-equilibrium statistical mechanics. This endeavor has garnered increasing attention in recent decades due to remarkable exact results from integrability and, more recently, from hydrodynamics. After a brief survey of past works, I will discuss several recent exact results from our work on macroscopic fluctuations (large deviations) in non-equilibrium states. These new results include current fluctuations of diffusive systems in various geometries, such as a semi-infinite line, an infinite line with defects, and a finite line with varied coupling to reservoirs. Additionally, I will discuss density fluctuations in the non-equilibrium stationary state of generic diffusive systems coupled with unequal reservoirs, emphasizing on the desired robustness of non-equilibrium fluctuations. Most of these results are based on fluctuating hydrodynamic descriptions, which I will elaborate on. I will conclude by presenting a robust approach for deriving this hydrodynamic description from microscopic dynamics, that extends even for active matter.