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arxiv: 2604.26093 · v1 · submitted 2026-04-28 · ❄️ cond-mat.stat-mech

Diffusion with conserved marginal distributions and information theory in fracton hydrodynamics

Vaibhav Mohanty , Sunghan Ro This is my paper

Pith reviewed 2026-05-07 14:21 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords diffusionsubsystem symmetriesfracton hydrodynamicsnonlinear hydrodynamicsmarginal distributionsinformation theoryshear transportmultipole conservation
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0 comments X

The pith

Subsystem symmetries generically produce nonlinear hydrodynamic equations that preserve localization in marginal distributions at long times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates diffusion when conservation laws apply only at the subsystem level rather than globally. It shows that subsystem symmetries generically yield nonlinear hydrodynamic equations featuring shear-only transport. Because marginal distributions are conserved, any initial localization within them remains intact at long times and does not spread. A linear regime appears solely as the limit of small fluctuations around a uniform background. The work derives the deterministic and fluctuating hydrodynamic equations in arbitrary dimensions, identifies the corresponding maximum-entropy equilibria, and supplies an information-theoretic reading in which total correlation decays monotonically even if pairwise mutual information does not.

Core claim

Subsystem symmetries generically produce nonlinear hydrodynamic equations with shear-only transport. Any localization present in the initial marginal distributions is preserved at long times by the conservation of those marginals. A linear regime emerges only as a limiting case for small fluctuations around a uniform background. The deterministic and fluctuating parts of the hydrodynamic equations are derived in arbitrary dimensions, along with the corresponding maximum-entropy equilibrium distributions under constrained marginals. Marginal-conserving diffusion provides a concrete hydrodynamic realization of partial multipole-moment conservation, with total correlation decaying monotonically

What carries the argument

Subsystem symmetries enforcing conservation of marginal distributions, which produce nonlinear diffusion equations with shear-only transport that preserve initial localizations.

Load-bearing premise

That conservation laws imposed only at the subsystem level generically yield nonlinear hydrodynamic equations rather than linear ones and that maximum-entropy distributions under marginal constraints are the appropriate equilibria.

What would settle it

Numerical simulation of the derived equations or a microscopic model with subsystem symmetries in which localized marginal distributions spread at long times would falsify the preservation claim.

Figures

Figures reproduced from arXiv: 2604.26093 by Sunghan Ro, Vaibhav Mohanty.

Figure 1
Figure 1. Figure 1: FIG. 1. Microscopic model for shear-only transport, where view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical results for two-dimensional marginal-conserving diffusion. (A) The initial distribution at view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Generalized microscopic model for (A) view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. KL divergence view at source ↗
read the original abstract

Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that conserving complete multipole-moment groups leads to subdiffusive dynamics governed by a nonlinear diffusion equation, raising the question of whether hydrodynamic equations would also be nonlinear when the conservation law is imposed only at the subsystem level. Here we show that subsystem symmetries generically produce nonlinear hydrodynamic equations with shear-only transport, in which any localization present in the initial marginal distributions is preserved at long times by the conservation of those marginals. A linear regime emerges only as a limiting case for small fluctuations around a uniform background. We derive the deterministic and fluctuating parts of the hydrodynamic equations in arbitrary dimensions and obtain the corresponding maximum-entropy equilibrium distributions under constrained marginals. We also show that marginal-conserving diffusion provides a concrete hydrodynamic realization of partial multipole-moment conservation, and we offer an information-theoretic interpretation in which total correlation decays monotonically even when pairwise mutual information does not.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 4 minor

Summary. The manuscript shows that imposing conservation laws only at the subsystem level (rather than on global multipole moments) generically yields nonlinear hydrodynamic equations with shear-only transport. Any localization present in the initial marginal distributions is preserved at long times by these conservation laws. The authors derive the deterministic and fluctuating hydrodynamic equations in arbitrary dimensions, obtain the corresponding maximum-entropy equilibria under the marginal constraints, interpret the dynamics as a hydrodynamic realization of partial multipole-moment conservation, and provide an information-theoretic reading in which total correlation decays monotonically.

Significance. If the derivations hold, the result supplies a concrete mechanism by which subsystem symmetries produce nonlinear, shear-dominated hydrodynamics and a preservation property for marginal localization. It bridges fracton hydrodynamics with information theory and offers a natural setting for partial multipole conservation. The explicit construction of fluctuating equations and max-ent equilibria under marginal constraints strengthens the link between symmetry, conservation, and long-time behavior, which is relevant to experiments in tilted optical lattices.

minor comments (4)
  1. §2.2, Eq. (17): the fluctuating term is written with a noise correlator that assumes white-in-time statistics; a brief justification for why colored noise would not alter the long-time marginal preservation would strengthen the fluctuating hydrodynamics section.
  2. §3.1: the maximum-entropy construction under marginal constraints is presented for continuous fields; an explicit discrete-lattice version (or a statement that the continuum limit commutes with the marginal projection) would clarify applicability to lattice models.
  3. Figure 2 caption: the plotted decay of total correlation versus pairwise mutual information lacks error bars or ensemble size; adding this information would make the numerical support for the information-theoretic claim easier to assess.
  4. The transition to the linear regime (small fluctuations around uniform background) is stated as a limiting case but is not accompanied by a dimensionless parameter that quantifies when nonlinearity becomes negligible; a short scaling argument would help readers identify the relevant regime.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive summary and recommendation of minor revision. The referee's overview correctly identifies the central results on subsystem symmetries, nonlinear shear-only hydrodynamics, preservation of marginal localization, maximum-entropy equilibria, partial multipole conservation, and the information-theoretic interpretation.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives its hydrodynamic equations directly from the imposition of subsystem symmetries and the resulting conservation of marginal distributions, without fitting parameters or re-using the target result as an input. The nonlinear structure, shear-only transport, and preservation of initial localization emerge as consequences of those conservation laws applied at the subsystem level. Maximum-entropy equilibria are constructed under the stated marginal constraints, and the information-theoretic interpretation follows from the derived dynamics. Background references to prior multipole-conservation results serve only as motivation and are not load-bearing for the subsystem-level claims. The logical chain is therefore self-contained and independent of the conclusions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on standard assumptions from hydrodynamics and statistical mechanics; no free parameters or new entities are mentioned.

axioms (2)
  • domain assumption The maximum-entropy principle applies to find equilibrium distributions under constrained marginals.
    Invoked to obtain the corresponding maximum-entropy equilibrium distributions.
  • domain assumption Subsystem symmetries imply conservation of marginal distributions at the hydrodynamic scale.
    Central to deriving the nonlinear equations from subsystem symmetries.

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Reference graph

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    (A1) Taking the functional derivative, we have δS δρ =−log ρ(x, y) q −1−λ−ϕ x(x)−ϕ y(y) = 0, (A2) which gives us ρ(x, y) =e lnq−1−λ−ϕ x(x)−ϕy(y)

    Two dimensions In two dimensions, we perform entropy maximization with the conservation ofxandymarginal distributions considered with Lagrange multipliers: S[ρ] =− Z dx Z dy ρ(x, y) log ρ(x, y) q +λ 1− Z dx Z dy ρ + Z dx ϕx(x) ρ(x)− Z dy ρ(x, y) + Z dy ϕy(y) ρ(y)− Z dx ρ(x, y) . (A1) Taking the functional derivative, we have δS δρ =−log ρ(x, y) q −1−λ−ϕ x...

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    KL divergence between initial and equilibrium distributions equals the entropy gap The KL divergence between the particle density distribution and the equilibrium distribution is DKL[ρ||ρeq] = Z ddrρ(r) log ρ(r) ρeq(r) = Z ddrρ(r) logρ(r)− Z ddrρ(r) logρ eq(r) =−S[ρ]− Z ddrρ(r) logρ eq(r) =−S[ρ] +S[ρ|ρ eq], (B3) whereS[ρ|ρ eq] is the cross-entropy between...

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