Universality and well-posedness for a time-inhomogeneous KPZ equation

This talk has two goals. The first is a derivation of a time-inhomogeneous KPZ equation from fluctuations in a Ginzburg–Landau SDE in nonequilibrium. The method is a fluctuation-scale analog of Yau's method for hydrodynamic limits in nonequilibrium. The second is well-posedness of the limit KPZ equation itself, which has a log nonlinearity that is absent in the time-homogeneous case. A number of questions in the spirit of nonequilibrium statistical mechanics (e.g., hysteresis in the microscopic model) will also be addressed, as well as further extensions.