Monitored Fluctuating Hydrodynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918343394459648 |
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| author | Gopalakrishnan, Sarang McCulloch, Ewan Vasseur, Romain |
| author_facet | Gopalakrishnan, Sarang McCulloch, Ewan Vasseur, Romain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monitored Fluctuating Hydrodynamics Gopalakrishnan, Sarang McCulloch, Ewan Vasseur, Romain Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics 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. |
| title | Monitored Fluctuating Hydrodynamics |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2504.02734 |