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arxiv: 2606.02391 · v1 · pith:2WXENPKBnew · submitted 2026-06-01 · ✦ hep-th · cond-mat.stat-mech· cond-mat.str-el

Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs

Luca V. Delacretaz This is my paper

Pith reviewed 2026-06-28 13:34 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechcond-mat.str-el
keywords fluctuating hydrodynamicseffective field theoryspontaneous symmetry breakingthermal dynamicstransport coefficientsgeneralized symmetriest Hooft anomaliesUV/IR constraints
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The pith

Fluctuating hydrodynamics emerges in nearly all local many-body systems at finite temperature through effective field theories organized by strong-to-weak spontaneous symmetry breaking.

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

The paper presents lectures that organize the equilibrium and out-of-equilibrium dynamics of thermalizing systems around the emergence of fluctuating hydrodynamics. It shows how modern EFT constructions achieve this by framing the process as strong-to-weak spontaneous symmetry breaking. The approach applies across examples from spin chains to relativistic quantum field theories, including cases with generalized symmetries and 't Hooft anomalies. It further derives UV/IR constraints on the transport parameters that serve as Wilson coefficients in these hydrodynamic EFTs.

Core claim

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature, and modern EFT constructions frame this emergence through the lens of strong-to-weak spontaneous symmetry breaking, enabling quantitative study of late-time observables in systems with generalized symmetries or 't Hooft anomalies while yielding UV/IR constraints on transport parameters both in the continuum and on the lattice.

What carries the argument

strong-to-weak spontaneous symmetry breaking, the organizing principle that constructs the hydrodynamic EFT by breaking symmetries from strong (UV) to weak (IR) form.

If this is right

  • Late-time observables become calculable in a controlled way for spin chains, relativistic QFTs, and models with generalized symmetries or anomalies.
  • Transport parameters obey specific UV/IR relations that hold both in continuum theories and on the lattice.
  • The same EFT construction supplies quantitative predictions for out-of-equilibrium dynamics in thermalizing systems.
  • Wilson coefficients of the hydrodynamic EFT can be constrained by matching to microscopic UV data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework could be used to derive hydrodynamic descriptions for systems whose symmetries are not yet fully classified.
  • Lattice simulations of spin chains could directly test the predicted relations among transport coefficients.
  • Extensions to systems with explicit breaking or to lower dimensions might reveal where the strong-to-weak paradigm requires additional terms.

Load-bearing premise

The strong-to-weak spontaneous symmetry breaking supplies a controlled and uniform framework that works for all the listed systems without extra uncontrolled approximations.

What would settle it

A concrete local many-body system at nonzero temperature in which late-time observables cannot be captured by any EFT built on strong-to-weak symmetry breaking, or in which the predicted UV/IR relations among transport coefficients are violated.

Figures

Figures reproduced from arXiv: 2606.02391 by Luca V. Delacretaz.

Figure 1
Figure 1. Figure 1: (a) Global equilibrium is reached after a time scale that grows with volume in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schwinger-Keldysh contour with sources. Time increases from left to right. [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) On-shell condition for the two internal legs, leading to a branch point at [PITH_FULL_IMAGE:figures/full_fig_p035_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Density two-point function ⟨n(t, x)n⟩ in a classical lattice gas from early times (blue) to late times (yellow), against the scaling variable y = x/√ Dt. In this model, χ(n) and D(n) are known analytically, so that the leading (F0,0) and subleading 1-loop (F1,0) EFT predictions from (4.37) are completely fixed. (a) Approximate scaling collapse of C(t, y) ≡ √ t⟨n(t, y)n⟩ towards the leading scaling function… view at source ↗
Figure 5
Figure 5. Figure 5: Original Schwinger-Keldysh contour (left) and its adaptations for the SFF (center) [PITH_FULL_IMAGE:figures/full_fig_p037_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Hydrodynamics cannot emerge too soon or it would violate microcausality [PITH_FULL_IMAGE:figures/full_fig_p047_6.png] view at source ↗
read the original abstract

Fluctuating hydrodynamics emerges in essentially any local many-body system at nonzero temperature. Effective field theory (EFT) approaches enable the quantitative study of this emergence, providing a controlled framework to capture late-time observables. These lectures introduce the organizing principles behind equilibrium and out-of-equilibrium dynamics in these thermalizing systems. A central focus is the modern construction of these EFTs, which frames fluctuating hydrodynamics through the lens of "strong-to-weak" spontaneous symmetry breaking. Drawing examples from both high-energy and condensed matter physics, we show how this paradigm adapts to systems ranging from spin chains to relativistic quantum field theories, including models with generalized symmetries or symmetries with 't Hooft anomalies. Finally, we discuss UV/IR constraints on transport parameters -- viewed as the Wilson coefficients of hydrodynamic EFTs -- both in continuum and on the lattice.

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 / 2 minor

Summary. The manuscript consists of lecture notes introducing the organizing principles of equilibrium and out-of-equilibrium dynamics in thermalizing many-body systems at nonzero temperature. It centers on constructing effective field theories for fluctuating hydrodynamics through the strong-to-weak spontaneous symmetry breaking paradigm, with examples drawn from spin chains, relativistic quantum field theories, systems with generalized symmetries, and those exhibiting 't Hooft anomalies. The notes conclude by discussing UV/IR constraints on transport parameters, treated as Wilson coefficients of the hydrodynamic EFTs.

Significance. If the exposition is accurate and accessible, these lectures could provide a useful synthesis of the strong-to-weak SSB framework for hydrodynamic EFTs, helping researchers connect concepts across high-energy and condensed-matter contexts. The emphasis on adaptability to generalized symmetries and anomalies, together with the treatment of transport coefficients as EFT Wilson coefficients, offers a coherent organizing perspective on late-time observables without introducing new theorems or quantitative predictions.

minor comments (2)
  1. The abstract refers to 'modern construction' of the EFTs but does not specify which sections contain the explicit symmetry-breaking pattern or the mapping to hydrodynamic variables; adding a short roadmap paragraph after the introduction would improve navigability for readers.
  2. When discussing lattice versus continuum UV/IR constraints, the notes should explicitly note whether any example calculations are provided or whether the discussion remains at the level of general principles.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and their recommendation to accept. We are pleased that the lectures are viewed as providing a useful synthesis of the strong-to-weak SSB framework across high-energy and condensed-matter contexts.

Circularity Check

0 steps flagged

No significant circularity; expository review of existing framework

full rationale

The document is a set of lecture notes that organizes and reviews the strong-to-weak spontaneous symmetry breaking construction for hydrodynamic EFTs, drawing on prior literature across spin chains, relativistic QFTs, and systems with generalized symmetries. No new central derivation, theorem, or quantitative prediction is advanced whose validity would reduce to a fitted parameter, self-citation chain, or definitional equivalence within the text itself. All load-bearing steps are presented as summaries of independently established results rather than as self-contained derivations that collapse by construction. The paper therefore remains self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; no explicit free parameters, new axioms, or invented entities are introduced in the summary. The framework rests on standard EFT and symmetry-breaking assumptions already present in the cited literature.

axioms (1)
  • domain assumption Spontaneous symmetry breaking can be applied in the strong-to-weak sense to describe the emergence of hydrodynamics in thermal systems.
    Invoked as the central organizing principle for the EFT construction.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Hydrodynamic tails in chaotic spin chains with quantum group symmetry

    cond-mat.stat-mech 2026-06 unverdicted novelty 7.0

    Quantum group symmetry enables superdiffusive hydrodynamic tails for transverse spin operators in chaotic XXZ-like models despite lacking local quantum group charges.

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