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Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter

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Alexios Christopoulos, João Costa, Stefano Scopa, Jacopo De Nardis, Zala Lenarčič, Denis Bernard, Tony Jin

Statistical Mechanics · Submitted 31 Aug 2026 · 109 references

Pith's verdict: First derivation of nonlinear MFT from a microscopic quantum model, but the factorization closure is unproven beyond second cumulants and the two fitted parameters make the theory semi-phenomenological rather than fully ab initio.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on September 9, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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arXiv ID2609.00159 (version 1)
Pith ID5LM24QGM, Pith's permanent record of this paper and its review
CitationAlexios Christopoulos, Denis Bernard, Jacopo De Nardis, Jo\~ao Costa, Stefano Scopa, Tony Jin, Zala Lenar\v{c}i\v{c}. "Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter." arXiv:2609.00159 (2026). https://pith.science/paper/5LM24QGM
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The paper

The paper claims

A macroscopic fluctuation theory with density-dependent transport coefficients is derived from the microscopic Lindblad dynamics of a dephasing XXZ spin chain and validated with tensor-network simulations.

The reading

Macroscopic Fluctuation Theory (MFT) is a classical framework that describes the large-scale behavior of diffusive systems using only two transport coefficients: diffusivity and mobility. For interacting quantum many-body systems, whether such a framework exists has been an open question. The paper considers a paradigmatic quantum model: a one-dimensional XXZ spin chain with bulk dephasing noise and boundary reservoirs, which drives the system to a non-equilibrium steady state. Starting from the full Lindblad master equation, they perform a strong-coupling expansion in the limit of large dephasing, which projects the dynamics onto diagonal states where coherences are suppressed. This yields an effective classical exclusion process called the Interacting Symmetric Exclusion Process (ISEP), where particles hop at rates that depend on the occupancy of next-nearest neighbor sites. By coarse-graining this process in the thermodynamic limit and assuming that density correlations factorize at leading order, a closed nonlinear diffusion equation emerges with a density-dependent diffusivity and mobility. These transport coefficients are linked by a fluctuation-dissipation relation, leaving the diffusivity to be determined. The diffusivity is expressed analytically in terms of two effective couplings, which are extracted numerically by fitting the stationary density profile. With these fitted parameters, the theory predicts the long-range density correlations and the full counting statistics of the current, matching tensor-network simulations of the original quantum model with high accuracy. The work demonstrates that noisy interacting quantum systems can exhibit the universality class of classical MFT with nonlinear transport coefficients.
Extended reading notes

Core claim

The paper claims the first explicit derivation of a nonlinear fluctuating hydrodynamics with density-dependent diffusivity and mobility, directly from the microscopic Lindblad dynamics of a boundary-driven XXZ spin chain with bulk dephasing, and that this hydrodynamics belongs to the universality class of classical Macroscopic Fluctuation Theory.

Load-bearing premise

The factorization assumption (Eq. 11) that density correlations obey the scaling ⟨n_i1 ... n_im⟩_c = O(N^{1-m}), which implies that operators with disjoint supports factorize at leading order in 1/N, is not rigorously proven and is crucial for closing the hierarchy of equations. This assumption is stated and used in the main text near Eq. (11) and is checked numerically only for second- and third-order cumulants, not for all orders.

Original abstract

A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,433 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. background 0.79 0.03 0.03 asserted 1.00
s1 Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. contribution 0.97 0.97 0.20 asserted 1.00
s2 Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. result 0.93 0.91 0.11 asserted 1.00
s3 This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. result 0.99 0.94 0.14 asserted 0.99
s4 Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems. interpretation 0.99 0.92 0.92 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Microscopic model and emergent stochastic dynamics. Top: XXZ spin chain with bulk dephasing and boundary reservoirs, driving the system to a NESS. Bottom: In the strong-coupling regime, the model reduces to the effective dynamics of the interacting sym￾metric exclusion process (ISEP), which describes non-overlapping particles whose jump rates depend on the next-nearest neighbor occu￾pation. systematic fluctuating hydrodynamic description of interacting diffusive quantum matter. Model and strategy— We first introduce the microscopic model. We consider the one-dimensional XXZ spin…
Figure 2. Numerical test of the ISEP description. Tensornetwork data for the Lindblad dynamics µ 03 and N ∈ {4070100200} (increasing N in darkening shades of blue)Red: MFT predicti Figure 2. Numerical test of the ISEP description. Tensornetwork data for the Lindblad dynamics µ = 03 and N ∈ {4070100200} (increasing N in darkening shades of blue)Red: MFT predicti gpy µ = 03 and N ∈ {4070100200} (increasing N in darkening shades of blue)Red: MFT predicti gpy µ = 03 and N ∈ {4070100200} (increasing N in darkening shades of blue)Red: MFT predicti Figure 2. Numerical test of the ISEP description.…
Figure 3. Finite-size scaling tests of the MFT description. (a) Connected spin correlator of the magnetization,

Figures reproduced from arXiv:2609.00159 by the authors.

References

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