Macroscopic fluctuation theory of stochastic systems undergoing monitoring
Abstract
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.
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BibTeX
@misc{costa2026macroscopic,
title = {{Macroscopic fluctuation theory of stochastic systems undergoing monitoring}},
author = {João Costa and Pedro Ribeiro and Andrea De Luca},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18500},
eprint = {2610.18500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18500},
}
RIS
TY - UNPB
TI - Macroscopic fluctuation theory of stochastic systems undergoing monitoring
AU - João Costa
AU - Pedro Ribeiro
AU - Andrea De Luca
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18500
UR - https://arxiv.org/abs/2610.18500
AB - 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.
ER -