Macroscopic fluctuation theory of stochastic systems undergoing monitoring

We develop a macroscopic fluctuation theory for diffusive classical lattice gases subject to continuous coarse-grained monitoring. Treating measurements in the typical-outcome (quenched) regime, we show that observation adds a quadratic confining term to the MFT action that pins the density to its hydrodynamic profile. We derive sufficient conditions under which, in the presence of monitoring, the current large-deviation function remains convex, the additivity principle holds, and dynamical phase transitions are excluded. For particle-hole-symmetric one-dimensional models we find that monitoring suppresses dynamical phase transitions and can change their order from second to first, as we demonstrate in the Katz–Lebowitz–Spohn model. In the strong-measurement limit, we find that the current distribution becomes Gaussian and determine the scaling of its cumulants: they follow simple power laws when the mobility remains nonzero throughout the system, but exhibit anomalous logarithmic scaling when the mobility vanishes at the boundaries.