Monitored Fluctuating Hydrodynamics
arXiv:2504.02734 · doi:10.1103/295c-lj1w
Abstract
We introduce a hydrodynamic framework for describing monitored classical stochastic processes. We study the conditional ensembles for these monitored processes -- i.e., we compute spacetime correlation functions conditioned on a fixed, typical measurement record. In the presence of global symmetries we show that these conditional ensembles can undergo measurement-induced "sharpening" phase transitions as a function of the monitoring rate; moreover, even weak monitoring can give rise to novel critical phases, derived entirely from a classical perspective. We give a simple hydrodynamic derivation of the known "charge-fuzzy phase" for weakly monitored diffusive many-body quantum systems. We show that although the unmonitored symmetric and asymmetric exclusion processes are in different universality classes of transport, the fluctuations in their conditional ensembles flow to the same fixed point with emergent relativistic invariance under monitoring. On the other hand, weakly monitored systems with non-Abelian symmetries enter a novel strongly coupled fixed point with non-trivial dynamical exponent, which we characterize. Our formalism naturally accounts for monitoring general observables, such as currents or density gradients, and allows for a direct calculation of information-theoretic diagnostics of sharpening transitions, including the Shannon entropy of the measurement record.
14 pages, 4 figures
References in corpus (78)
- Efficient classical simulation of slightly entangled quantum computations
- The large deviation approach to statistical mechanics
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Macroscopic fluctuation theory
- Measurement-driven entanglement transition in hybrid quantum circuits
- Theory of the phase transition in random unitary circuits with measurements
- Measurement-induced criticality in random quantum circuits
- Random Quantum Circuits
- Unitary-projective entanglement dynamics
- Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
- Dynamic first-order phase transition in kinetically constrained models of glasses
- Dynamical purification phase transitions induced by quantum measurements
- Critical properties of the measurement-induced transition in random quantum circuits
- First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Thermodynamic formalism for systems with Markov dynamics
- Direct evaluation of large-deviation functions
- Scalable probes of measurement-induced criticality
- Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
- Entanglement transition from variable-strength weak measurements
- Emergent statistical mechanics of entanglement in random unitary circuits
- Fracton hydrodynamics
- Entanglement phase transitions in measurement-only dynamics
- Measurement-induced topological entanglement transitions in symmetric random quantum circuits
- The one-dimensional KPZ equation and its universality class
- Entanglement Transitions from Holographic Random Tensor Networks
- Statistical mechanics of quantum error correcting codes
- Measurement Protected Quantum Phases
- Postselection-free entanglement dynamics via spacetime duality
- Simulating rare events in dynamical processes
- Self-Organized Error Correction in Random Unitary Circuits with Measurement
- Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
- Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
- Quantum criticality under decoherence or weak measurement
- Entanglement and purification transitions in non-Hermitian quantum mechanics
- Conformal invariance and quantum non-locality in critical hybrid circuits
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Operator scaling dimensions and multifractality at measurement-induced transitions
- Symmetry enriched phases of quantum circuits
- The Exclusion Process: A paradigm for non-equilibrium behaviour
- Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
- Spacetime duality between localization transitions and measurement-induced transitions
- Cross Entropy Benchmark for Measurement-Induced Phase Transitions
- Nonlinear sigma models for monitored dynamics of free fermions
- Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
- Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
- Controlling entanglement at absorbing state phase transitions in random circuits
- Transitions in the learnability of global charges from local measurements
- Entanglement transitions with free fermions
- Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization
- Scrambling Transition in a Radiative Random Unitary Circuit
- Measurement-induced purification in large-N hybrid Brownian circuits
- Entanglement Steering in Adaptive Circuits with Feedback
- Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
- Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with symmetry
- Purification Timescales in Monitored Fermions
- Dynamical simulations of classical stochastic systems using matrix product states
- Triviality of quantum trajectories close to a directed percolation transition
- Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
- Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
- Measurement-induced phase transitions on dynamical quantum trees
- Measurement-induced phase transition in a classical, chaotic many-body system
- Measurement-induced transitions for interacting fermions
- Entanglement Structure and Information Protection in Noisy Hybrid Quantum Circuits
- Infinite-randomness criticality in monitored quantum dynamics with static disorder
- Noise-induced phase transitions in hybrid quantum circuits
- Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
- Observing quantum measurement collapse as a learnability phase transition
- Bridging the gap between classical and quantum many-body information dynamics
- Measurement-induced phase transitions in the toric code
- Boundary transfer matrix spectrum of measurement-induced transitions
- Renormalization group for measurement and entanglement phase transitions
- Measurement-induced phase transition in a single-body tight-binding model
- Field theory of monitored, interacting fermion dynamics with charge conservation
- Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
- Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality
- Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer