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Local-equilibrium theory of neutrino oscillations

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues that neutrino flavor mixing in astrophysical environments can be closed at coarse-grained scales by a turbulent flavor-wave viscosity, computable from a kinetic theory of weakly coupled collective neutrino excitations.

desk verdict Promising framework for nonadiabatic neutrino transport, but the advertised kinetic closure for flavor viscosity is not actually derived—Eq. (39) remains formal. read the letter →

arxiv 2506.03271 v1 pith:ULBD3GME submitted 2025-06-03 hep-ph astro-ph.HE

Lucas Johns , Anson Kost This is my paper
classification hep-phastro-ph.HE PACS 14.60.Pq
keywords neutrinooscillationsmiscidynamicsflavor-waveviscositywavekineticsflavorinstabilitiescoarse-grainedtransportlocalmixingequilibriumquantumkineticequations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

In dense astrophysical settings such as core-collapse supernovae and neutron-star mergers, neutrino flavor oscillations occur on sub-millimeter scales while the surrounding fluid changes over kilometers, making direct simulation of the quantum kinetic equations impossible. This paper extends miscidynamics, a coarse-grained transport theory that assumes neutrinos sit near local mixing equilibrium, beyond its earlier adiabatic limit by adding subgrid flavor waves and the turbulent flavor-wave viscosity they exert on the mean flavor state. The authors show that in the quasistatic limit the mean polarization obeys $(\partial_t + \hat{q}\cdot\partial_r)P_{\rm eq}^q = -(\gamma_q + \Gamma_q)P_{\rm eq}^q$, and they develop a wave-kinetic closure for $\gamma_q$ in terms of neutrino decay into flavor waves, the inverse fusion process, and three-wave scattering. If the closure holds, neutrino flavor transport can be simulated at astrophysical scales without resolving the fine-grained oscillation dynamics, and flavor evolution is governed by a competition between entropy-increasing viscosity and order-promoting collisional effects.

What carries the argument

The central object is the flavor wave: a subgrid Fourier mode $P_{q,n\neq0}$ of the neutrino polarization field, viewed as a weakly coupled emergent quasiparticle analogous to a phonon or plasmon. Its generator is the $3N\times3N$ non-Hermitian matrix $H_n$, built from the coarse-grained polarizations and the geometric factor $f_{q_i,q_j}=1-\hat{q}_i\cdot\hat{q}_j$, whose eigenvalues $\Omega_{n,i}$ give the flavor-wave dispersion relation and whose eigenvectors carry full three-component polarization information. The argument is carried by three approximation steps: weak-inhomogeneity linearization, which drops quadratic terms in $P_{q,n\neq0}$ and works on any mixing-equilibrium background, including resonance and spectral-swap configurations; the secular approximation, which retains only resonant interactions satisfying $\Omega^R_{n-m,j}+\Omega^R_{m,l}=\Omega^R_{n,i}$ for three-wave scattering and $\Omega^R_{-n,i}+\Omega^R_{n,i}=0$ for neutrino decay, the latter being always kinematically allowed; and the ray approximation with the quasistatic assumption for propagating waves through the slowly varying background.

What would settle it

A direct numerical check: evolve the quantum kinetic equation in a periodic box through a weakly unstable mixing equilibrium that is driven slowly by collisions, measure the coarse-grained depolarization rate, and compare it with the eigenmode-sum prediction for $\gamma_q$ in Eq. (79); quantitative disagreement, or a depolarization rate that jumps discontinuously as the driving passes a spectral degeneracy, would falsify the quasistatic kinetic closure. A second check: locate the exceptional points of $H_n$ along a realistic supernova trajectory, since generically closing band gaps at operating densities would break the approximation exactly where the theory is needed.

Watch

Extended reading notes

Core claim

The central claim is that the coarse-grained neutrino polarization in local mixing equilibrium evolves, in the quasistatic limit, as $(\partial_t + \hat{q}\cdot\partial_r)P_{\rm eq}^q = -(\gamma_q + \Gamma_q)P_{\rm eq}^q$ in the local equilibrium frame, where $\gamma_q$ is the turbulent flavor-wave viscosity produced by subgrid correlations and $\Gamma_q$ is the collisional depolarization rate. This viscosity is nonvanishing even at infinite scale separation between oscillation and astrophysical lengths, because subgrid correlations are driven by the astrophysical background itself. To close $\gamma_q$ without solving the full quantum kinetic equation, the paper introduces weak-inhomogeneity linear analysis, which treats the off-equilibrium Fourier modes $P_{q,n\neq0}$ as small while allowing the background polarizations to point in any direction; the resulting non-Hermitian Hamiltonian $H_n$ defines flavor waves as collective quasiparticles with a band structure $\Omega_{n,i}$. A secular approximation then yields kinetic equations in which neutrinos decay into pairs of flavor waves, flavor waves fuse back into neutrinos, and three flavor waves scatter, with energy and momentum conservation enforced by resonance conditions; flavor waves are transported along rays through Hamilton's equations. The paper further proposes that these processes generically do not lead to full flavor thermalization, because the same coarse-grained oscillation invariants that define local mixing equilibrium emerge dynamically and restrict the accessible flavor states.

Load-bearing premise

The load-bearing premise is the quasistatic approximation, that the slowly varying astrophysical background induces no transitions between flavor-wave energy bands, together with the scaling assumption that subgrid correlations are only as large as the astrophysical driving rate; the paper itself warns that the quasistatic part is probably inapplicable in many cases because exceptional points can close band gaps no matter how slow the driving is.

Editorial extensions

If this is right

  • Nonadiabatic flavor evolution persists in the limit of infinite scale separation: $\gamma_q$ is tied to the astrophysical driving rate, so flavor viscosity survives even as the oscillation length goes to zero compared with the grid scale.
  • The flavor-wave kinetic scheme supplies a concrete closure for the hierarchy of subgrid correlation moments, so the mean transport equations can be advanced on astrophysical time steps without resolving oscillation-scale dynamics.
  • Weak-inhomogeneity linear analysis extends flavor-wave theory to equilibrium backgrounds that are not aligned with the flavor axis, and it retains complete polarization-vector information rather than only small flavor coherences.
  • If $\gamma_q>0$ the coarse-grained system heats up as neutrinos decay into flavor waves, while $\gamma_q<0$ corresponds to fusion of waves back into neutrinos; the authors conjecture that local oscillation invariants obstruct complete flavor thermalization, so equilibria are generically nonthermal.
  • Distinguishing adiabaticity from quasistaticity implies that spectral degeneracies, the exceptional points of the flavor-wave eigensystem, can produce non-quasistatic band transitions that constitute a separate and as yet unmodeled form of nonadiabaticity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial: The kinetic closure suggests a numerical test that the paper does not perform: solve the quantum kinetic equation in a periodic box, drive the background slowly through a weakly unstable equilibrium, measure the depolarization rate from Eq. (39), and compare it with the eigenmode-sum prediction of Eq. (79).
  • Editorial: Because three-wave scattering conserves energy and momentum, the flavor-wave spectrum may develop a wave-turbulence cascade; the observed high-$|k|$ exponential tails in simulation power spectra would then be the thermal, maximum-entropy part of the spectrum rather than a cascade, and the two are distinguishable by their scaling behavior.
  • Editorial: The analogy with turbulent eddy viscosity suggests a cheaper closure than full wave kinetics, such as a mixing-length parameterization of $\gamma_q$ in terms of local oscillation invariants; whether such a model is accurate is a testable question the paper leaves open.
  • Editorial: If exceptional points are generic in the flavor-wave spectrum, a transition-probability formula for avoided band crossings could turn the quasistatic approximation's main failure mode into a calculable correction, extending the theory to the non-quasistatic regime the authors defer.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a nonadiabatic extension of miscidynamics, a coarse-grained theory of neutrino flavor transport, by introducing a turbulent flavor-wave viscosity γq that captures the grid-level effect of subgrid flavor waves. The authors develop a weak-inhomogeneity linearization of the quantum kinetic equation that generalizes small-coherence linear analysis, derive the flavor-wave dispersion relation as an eigensystem problem for a non-Hermitian Hamiltonian, and outline a wave-kinetic description based on the secular approximation and a geometric-optics ray treatment for flavor-wave transport. They also discuss thermodynamic consequences, including the distinction between mixing equilibrium and flavor-wave equilibrium and the possible obstruction of flavor thermalization by emergent invariants.

Significance. The paper is significant in its ambition: a practical closure for nonadiabatic neutrino transport would be a major step for supernova and neutron-star-merger simulations. The weak-inhomogeneity linear analysis is a genuine generalization of existing methods and could be useful independently, and the authors are commendably honest about limitations, explicitly flagging the quasistatic approximation as likely inapplicable near exceptional points. The paper does not fit parameters to data and its speculative claims are presented as hypotheses. However, the central claim that a kinetic closure for γq is derived is not supported by the equations presented, which stop at an unclosed amplitude-level description; the value of the paper currently lies more in its conceptual framework and the specific open problems it identifies than in a usable closure.

major comments (3)
  1. [Sec. V.B (Eq. 79)] The central claim that Sec. V.B provides a kinetic closure for the turbulent flavor-wave viscosity γq in Eq. (39) is not carried through. Equation (79) defines γq as a sum over eigenmodes, but this sum is never evaluated after the secular approximation; the paper only states that the relative phases drop out and then discusses resonance conditions. The kinetic equations in Sec. V.C, Eqs. (88)-(90), evolve the full complex amplitude Φ_i and still contain the three-wave term N_i, which depends on products of amplitudes and phases. No Boltzmann-like collision integral or equation for an occupation number such as |A_{n,i}|² or the Wigner function R_k introduced in Sec. IV.C is derived. Consequently, Eq. (39) is a formal identity rather than a usable closure, and the hierarchy described in Sec. III.C remains open. The authors should either derive the explicit kinetic equation for the wave action or revise the claims to state that the closure is only outlined.
  2. [Sec. V.C] The quasistatic approximation, in which transitions between flavor-wave bands are neglected, is acknowledged in the paper to be "probably inapplicable in many cases," especially in the presence of unstable flavor waves and exceptional points. Since the central miscidynamic equation (39) is derived under this approximation, the domain of validity of the proposed theory is unclear. The paper should state a quantitative condition under which quasistaticity holds, such as a small dimensionless parameter measuring the rate of variation of the background relative to the level spacing, or should clearly delimit the regime of applicability. As it stands, the theory may not apply to the flavor instabilities that motivate the work.
  3. [Sec. II.B (Eq. 23)] The scaling assumption cq ∼ O(lastro) is posited without justification, and it is load-bearing because it is what allows γq to be treated as a grid-level term and to be of order 1/lastro. The paper excludes the strong-instability regime cq ≫ O(lastro) but provides no heuristic or numerical argument for why weak instabilities should satisfy this scaling. Without such support, the assumption remains an ad hoc input that limits the predictive power of the theory.
minor comments (5)
  1. [Sec. III.B (Eqs. 29-34)] The notation Cq is used both for the nonadiabatic frame generator in Eq. (31) and (in the form iCq) for the collision term in Eq. (1); this is confusing and should be changed, for example by using a different symbol for the frame term.
  2. [Sec. II.B (Eq. 36)] The symbol cq,non is reused in Eq. (36) for both a vector (first line) and a matrix or operator (third line), which is a notation error that should be fixed.
  3. [Sec. I (after Eq. 2)] There is a typo: "evauated" should be "evaluated."
  4. [Sec. V.B (Eq. 74)] The approximation φn,i ≈ φ0 - Ω_R t is said to rely on the smallness of N/|A| and Ω_I relative to Ω_R, but the conditions are not quantified; a brief statement of the expected scales would improve rigor.
  5. [Sec. VI (general)] The paper would benefit from a concrete worked example, such as a single unstable mode in a simplified spectrum, illustrating how the formalism would be applied in practice; currently the discussion remains at a formal level.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central equation is a definitional decomposition with an openly stated closure problem, not a fitted or self-cited prediction.

full rationale

The paper's central equation (39) is obtained by splitting the coarse-grained QKE in the local equilibrium frame and defining the depolarization rates via Eq. (40). This is an exact algebraic rearrangement: gamma_q is the projection of the subgrid correlation term c_eq onto P_eq, and the equation carries no content until a closure is supplied. No parameter is fitted to data, and no previously computed output is fed back as an input. The later reformulation of gamma_q in Eq. (79) and the secular-approximation treatment in Sec. V.B re-express the same correlation term in the eigenbasis of the flavor-wave Hamiltonian; this is a self-consistent closure ansatz, not a circular definition. The derivation does not depend on Refs. [51,52] for any decisive mathematical step beyond terminology; those works define the miscidynamics framework being extended, and the present results are derived from the QKE and explicitly stated approximations (weak inhomogeneity, secular approximation, quasistatic evolution). The paper candidly flags the quasistatic approximation as 'probably inapplicable in many cases' (Sec. V.C) and acknowledges that non-quasistatic transitions and a fully Boltzmann-like closure for the wave action are left for future work. Those are completeness and validity limitations, not circular reasoning, and no circular step can be exhibited from the paper's equations or citations.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The framework rests on the miscidynamics equilibrium hypothesis and several scaling approximations. It introduces no fitted numerical parameters; the only adjustable model parameter is the unspecified collisional damping rate Dq used for illustration. No new fundamental entities are postulated: flavor waves are emergent quasiparticles from the linearized QKE, and flavor-wave viscosity is a transport coefficient.

free parameters (1)
  • Dq (collisional depolarization rate)
    Introduced in Sec. IV.B as a simple model for the collision term Cq,n = -Dq Pq,n. No value is assigned; it enters the flavor-wave Hamiltonian (Eq. 49) but is not used in final quantitative results.
assumptions (6)
  • domain assumption Local mixing equilibrium: the coarse-grained density matrix ⟨ρq⟩ is everywhere close to a state satisfying [H_q^eq, ρ_q^eq] = 0.
    Sec. II.A defines miscidynamics; requires ⟨H_q⟩ × ⟨P_q⟩ = 0. The entire framework is invalid if the coarse-grained state is far from such equilibrium.
  • ad hoc to paper Subgrid correlations cq are of order lastro and therefore small compared with oscillation-scale terms.
    Posited in Sec. II.B; excludes strong flavor instabilities and is required for |Pq| and ϵq to be approximate invariants, a prerequisite for the miscidynamic equations.
  • ad hoc to paper Quasistatic approximation: the frame transformation Uq satisfies Cq ≈ 0, and flavor-wave level transitions are neglected.
    Adopted in Sec. III.B and V.C. The paper itself cautions that this is probably inapplicable near exceptional points, where unsuppressed transitions invalidate the kinetic closure.
  • domain assumption Weak inhomogeneity: Fourier modes Pq,n with n ≠ 0 are small, so quadratic terms can be dropped.
    Used in Sec. IV.B to linearize the QKE; converts the problem to a non-Hermitian eigensystem for flavor-wave modes.
  • standard math Secular approximation: rapidly oscillating terms average out; only resonant triads satisfying energy conservation are retained.
    Standard wave-kinetics reduction applied in Sec. V.B (Eq. 77), required for the kinetic closure.
  • ad hoc to paper Flavor waves propagate along rays according to Hamilton's equations.
    Geometric-optics approximation in Sec. V.C (Eq. 85). The derivation is informal, and the paper notes a more rigorous Wigner-function approach is possible.

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Cite this review

Pith. "Pith review of Local-equilibrium theory of neutrino oscillations." pith.science (2026). https://pith.science/paper/ULBD3GME

@misc{pith2026250603271,
  author       = {Pith},
  title        = {Pith review of: Local-equilibrium theory of neutrino oscillations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ULBD3GME}},
  note         = {Machine review of arXiv:2506.03271}
}
read the original abstract

Miscidynamics describes coarse-grained neutrino transport under the assumption that flavor mixing is in local equilibrium. Here we introduce the concept of turbulent flavor-wave viscosity and develop techniques for including it in miscidynamics. This extension of the theory is necessary when neutrinos develop weak flavor instabilities as a result of astrophysical driving. The flavor-wave dispersion relation is obtained using a new and more general form of linear analysis, which does not require small flavor coherence. Flavor-wave transport is then approximated using wave kinetics and geometric optics. We hypothesize that the dynamical emergence of local oscillation invariants restricts the extent of flavor thermalization. In this view, flavor evolution is sculpted by both entropy-increasing and order-promoting factors.

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Forward citations

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Reference graph

Works this paper leans on

100 extracted references · 53 canonical work pages · cited by 3 Pith papers

  1. [1]

    due to the appearance of exceptional points in the flavor-wave spectra. When Ω i and Ω j are degenerate, transitions between the two eigenmodes are unsuppressed and the evolution may be non-quasistatic regardless of how slow the astrophysical driving is. We leave for future work the development of techniques for dealing with non- quasistatic dynamics. VI....

  2. [2]

    R. F. Sawyer, Phys. Rev. Lett. 116, 081101 (2016)

    2016

  3. [3]

    Wu, Y.-Z

    M.-R. Wu, Y.-Z. Qian, G. Mart ´ ınez-Pinedo, T. Fischer, and L. Huther, Phys. Rev. D 91, 065016 (2015)

    2015

  4. [4]

    Wu and I

    M.-R. Wu and I. Tamborra, Phys. Rev. D 95, 103007 (2017)

    2017

  5. [5]

    M.-R. Wu, I. Tamborra, O. Just, and H.-T. Janka, Phys. Rev. D 96, 123015 (2017)

    2017

  6. [6]

    Abbar, H

    S. Abbar, H. Duan, K. Sumiyoshi, T. Takiwaki, and M. C. Volpe, Phys. Rev. D 100, 043004 (2019)

    2019

  7. [7]

    Delfan Azari, S

    M. Delfan Azari, S. Yamada, T. Morinaga, W. Iwakami, H. Okawa, H. Nagakura, and K. Sumiyoshi, Phys. Rev. D 99, 103011 (2019)

    2019

  8. [8]

    Morinaga, H

    T. Morinaga, H. Nagakura, C. Kato, and S. Yamada, Phys. Rev. Res. 2, 012046 (2020)

    2020

Show all 100 references
  1. [9]

    Xiong, A

    Z. Xiong, A. Sieverding, M. Sen, and Y.-Z. Qian, Astro- phys. J. 900, 144 (2020)

    2020

  2. [10]

    Ko, M.-K

    H. Ko, M.-K. Cheoun, E. Ha, M. Kusakabe, T. Hayakawa, H. Sasaki, T. Kajino, M.-a. Hashimoto, M. Ono, M. D. Usang, S. Chiba, K. Nakamura, A. Tol- stov, K. Nomoto, T. Kawano, and G. J. Mathews, Astro- phys. J. Lett. 891, L24 (2020)

    2020

  3. [11]

    George, M.-R

    M. George, M.-R. Wu, I. Tamborra, R. Ardevol-Pulpillo, and H.-T. Janka, Phys. Rev. D 102, 103015 (2020)

    2020

  4. [12]

    Abbar, F

    S. Abbar, F. Capozzi, R. Glas, H.-T. Janka, and I. Tam- borra, Phys. Rev. D 103, 063033 (2021)

    2021

  5. [13]

    Nagakura, A

    H. Nagakura, A. Burrows, L. Johns, and G. M. Fuller, Phys. Rev. D 104, 083025 (2021)

    2021

  6. [14]

    Tamborra and S

    I. Tamborra and S. Shalgar, Annu. Rev. Nucl. Part. Sci. 71 (2021)

    2021

  7. [15]

    Johns, Phys

    L. Johns, Phys. Rev. Lett. 130, 191001 (2023), arXiv:2104.11369 [hep-ph]

    2023 arXiv

  8. [16]

    Li and D

    X. Li and D. M. Siegel, Phys. Rev. Lett. 126, 251101 (2021)

    2021

  9. [17]

    O. Just, S. Abbar, M.-R. Wu, I. Tamborra, H.-T. Janka, and F. Capozzi, Phys. Rev. D 105, 083024 (2022)

    2022

  10. [18]

    Fern´ andez, S

    R. Fern´ andez, S. Richers, N. Mulyk, and S. Fahlman, Phys. Rev. D 106, 103003 (2022)

    2022

  11. [19]

    Fujimoto and H

    S.-i. Fujimoto and H. Nagakura, Mon. Not. R. Astron. Soc. 519, 2623 (2023)

    2023

  12. [20]

    Xiong, L

    Z. Xiong, L. Johns, M.-R. Wu, and H. Duan, Phys. Rev. D 108, 083002 (2023)

    2023

  13. [21]

    J. Liu, R. Akaho, A. Ito, H. Nagakura, M. Zaizen, and S. Yamada, Phys. Rev. D 108, 123024 (2023)

    2023

  14. [22]

    Ehring, S

    J. Ehring, S. Abbar, H.-T. Janka, G. Raffelt, and I. Tam- borra, Phys. Rev. Lett. 131, 061401 (2023)

    2023

  15. [23]

    Ehring, S

    J. Ehring, S. Abbar, H.-T. Janka, G. Raffelt, and I. Tamborra, Phys. Rev. D 107, 103034 (2023), arXiv:2301.11938 [astro-ph.HE]

    2023 arXiv

  16. [24]

    Ehring, S

    J. Ehring, S. Abbar, H. Janka, G. Raffelt, K. Naka- mura, K. Kotake, et al., arXiv preprint arXiv:2412.02750 (2024)

    2024

  17. [25]

    Froustey, S

    J. Froustey, S. Richers, E. Grohs, S. D. Flynn, F. Foucart, J. P. Kneller, and G. C. McLaughlin, Phys. Rev. D 109, 043046 (2024)

    2024

  18. [26]

    Akaho, J

    R. Akaho, J. Liu, H. Nagakura, M. Zaizen, and S. Ya- mada, Phys. Rev. D 109, 023012 (2024)

    2024

  19. [27]

    J. Liu, H. Nagakura, R. Akaho, A. Ito, M. Zaizen, S. Furusawa, and S. Yamada, Phys. Rev. D 110, 043039 (2024)

    2024

  20. [28]

    Mukhopadhyay, J

    P. Mukhopadhyay, J. Miller, and G. C. McLaughlin, As- trophys. J. 974, 110 (2024)

    2024

  21. [29]

    Y. Qiu, D. Radice, S. Richers, and M. Bhattacharyya, arXiv preprint arXiv:2503.11758 (2025)

    2025 arXiv

  22. [30]

    Wang and A

    T. Wang and A. Burrows, arXiv preprint arXiv:2503.04896 (2025)

    2025 arXiv

  23. [31]

    K. A. Lund, P. Mukhopadhyay, J. M. Miller, and G. McLaughlin, arXiv preprint arXiv:2503.23727 (2025)

    2025 arXiv

  24. [32]

    K. Mori, T. Takiwaki, K. Kotake, and S. Horiuchi, arXiv preprint arXiv:2501.15256 (2025)

    2025 arXiv

  25. [33]

    Abbar and M

    S. Abbar and M. C. Volpe, Phys. Rev. D 111, 083005 (2025)

    2025

  26. [34]

    M. C. Volpe, Rev. Mod. Phys. 96, 025004 (2024)

    2024

  27. [35]

    Tamborra, arXiv preprint arXiv:2412.09699 (2024)

    I. Tamborra, arXiv preprint arXiv:2412.09699 (2024)

    2024 arXiv

  28. [36]

    Johns, S

    L. Johns, S. Richers, and M.-R. Wu, arXiv preprint arXiv:2503.05959 (2025)

    2025 arXiv

  29. [37]

    Sigl and G

    G. Sigl and G. Raffelt, Nucl. Phys. B 406, 423 (1993). 16

    1993

  30. [38]

    Vlasenko, G

    A. Vlasenko, G. M. Fuller, and V. Cirigliano, Phys. Rev. D 89, 105004 (2014)

    2014

  31. [39]

    Stirner, G

    T. Stirner, G. Sigl, and G. Raffelt, J. Cosmol. Astropart. Phys. 2018 (05), 016

    2018

  32. [40]

    S. A. Richers, G. C. McLaughlin, J. P. Kneller, and A. Vlasenko, Phys. Rev. D 99, 123014 (2019)

    2019

  33. [41]

    Johns, H

    L. Johns, H. Nagakura, G. M. Fuller, and A. Burrows, Phys. Rev. D 101, 043009 (2020)

    2020

  34. [42]

    Johns, H

    L. Johns, H. Nagakura, G. M. Fuller, and A. Burrows, Phys. Rev. D 102, 103017 (2020)

    2020

  35. [43]

    Bhattacharyya and B

    S. Bhattacharyya and B. Dasgupta, Phys. Rev. D 102, 063018 (2020)

    2020

  36. [44]

    Bhattacharyya and B

    S. Bhattacharyya and B. Dasgupta, Phys. Rev. Lett.126, 061302 (2021), arXiv:2009.03337 [hep-ph]

    2021 arXiv

  37. [45]

    M.-R. Wu, M. George, C.-Y. Lin, and Z. Xiong, Phys. Rev. D 104, 103003 (2021), arXiv:2108.09886 [hep-ph]

    2021 arXiv

  38. [46]

    Richers, D

    S. Richers, D. Willcox, and N. Ford, Phys. Rev. D 104, 103023 (2021), arXiv:2109.08631 [astro-ph.HE]

    2021 arXiv

  39. [47]

    Nagakura, Phys

    H. Nagakura, Phys. Rev. D 106, 063011 (2022)

    2022

  40. [48]

    Xiong, M.-R

    Z. Xiong, M.-R. Wu, G. Mart ´ ınez-Pinedo, T. Fischer, M. George, C.-Y. Lin, and L. Johns, Phys. Rev. D 107, 083016 (2023), arXiv:2210.08254 [astro-ph.HE]

    2023 arXiv

  41. [49]

    Shalgar and I

    S. Shalgar and I. Tamborra, Phys. Rev. D 108, 043006 (2023), arXiv:2206.00676 [astro-ph.HE]

    2023 arXiv

  42. [50]

    Shalgar and I

    S. Shalgar and I. Tamborra, Phys. Rev. D 107, 063025 (2023)

    2023

  43. [51]

    Nagakura, L

    H. Nagakura, L. Johns, and M. Zaizen, Phys. Rev. D 109, 083013 (2024), arXiv:2312.16285 [astro-ph.HE]

    2024 arXiv

  44. [52]

    Johns, arXiv preprint arXiv:2306.14982 (2023)

    L. Johns, arXiv preprint arXiv:2306.14982 (2023)

    2023

  45. [53]

    Johns, arXiv preprint arXiv:2401.15247 (2024)

    L. Johns, arXiv preprint arXiv:2401.15247 (2024)

    2024 arXiv

  46. [54]

    Xiong, M.-R

    Z. Xiong, M.-R. Wu, M. George, C.-Y. Lin, N. K. Largani, T. Fischer, and G. Mart ´ ınez-Pinedo, Phys. Rev. D 109, 123008 (2024), arXiv:2402.19252 [astro-ph.HE]

    2024 arXiv

  47. [55]

    Xiong, M.-R

    Z. Xiong, M.-R. Wu, M. George, and C.-Y. Lin, Phys. Rev. Lett. 134, 051003 (2025)

    2025

  48. [56]

    D. F. G. Fiorillo, I. Padilla-Gay, and G. G. Raffelt, Phys. Rev. D 109, 063021 (2024)

    2024

  49. [57]

    D. F. G. Fiorillo and G. G. Raffelt, Phys. Rev. Lett. 133, 221004 (2024), arXiv:2403.12189 [hep-ph]

    2024 arXiv

  50. [58]

    D. F. Fiorillo and G. G. Raffelt, arXiv preprint arXiv:2502.06935 (2025)

    2025 arXiv

  51. [59]

    J. Liu, H. Nagakura, M. Zaizen, L. Johns, R. Akaho, and S. Yamada, Phys. Rev. D 111, 023051 (2025)

    2025

  52. [60]

    Abbar, M.-R

    S. Abbar, M.-R. Wu, and Z. Xiong, Phys. Rev. D 109, 043024 (2024)

    2024

  53. [61]

    Richers, J

    S. Richers, J. Froustey, S. Ghosh, F. Foucart, and J. Gomez, Phys. Rev. D 110, 103019 (2024)

    2024

  54. [62]

    J. P. Kneller, J. Froustey, E. B. Grohs, F. Foucart, G. C. McLaughlin, and S. Richers, Phys. Rev. D 111, 063046 (2025)

    2025

  55. [63]

    Froustey, J

    J. Froustey, J. P. Kneller, and G. C. McLaughlin, Phys. Rev. D 111, 063022 (2025)

    2025

  56. [64]

    Zaizen, Phys

    M. Zaizen, Phys. Rev. D 111, 103029 (2025)

    2025

  57. [65]

    Nagakura, M

    H. Nagakura, M. Zaizen, J. Liu, and L. Johns, Phys. Rev. D 111, 043028 (2025)

    2025

  58. [66]

    J. Liu, H. Nagakura, M. Zaizen, L. Johns, and S. Ya- mada, arXiv preprint arXiv:2503.18145 (2025)

    2025 arXiv

  59. [67]

    Banerjee, A

    A. Banerjee, A. Dighe, and G. Raffelt, Phys. Rev. D 84, 053013 (2011)

    2011

  60. [68]

    Izaguirre, G

    I. Izaguirre, G. Raffelt, and I. Tamborra, Phys. Rev. Lett. 118, 021101 (2017)

    2017

  61. [69]

    H. Duan, G. M. Fuller, and Y.-Z. Qian, J. Phys. G 36, 105003 (2009)

    2009

  62. [70]

    H. Duan, J. D. Martin, and S. Omanakuttan, Phys. Rev. D 104, 123026 (2021)

    2021

  63. [71]

    D. F. G. Fiorillo and G. G. Raffelt, J. High Energ. Phys. 2024 (225)

    2024

  64. [72]

    S. P. Mikheyev and A. Y. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985)

    1985

  65. [73]

    H. Duan, G. M. Fuller, J. Carlson, and Y.-Z. Qian, Phys. Rev. D 74, 105014 (2006)

    2006

  66. [74]

    H. Duan, G. M. Fuller, J. Carlson, and Y.-Z. Qian, Phys. Rev. Lett. 97, 241101 (2006)

    2006

  67. [75]

    G. G. Raffelt and A. Y. Smirnov, Phys. Rev. D 76, 125008 (2007)

    2007

  68. [76]

    G. G. Raffelt and A. Y. Smirnov, Phys. Rev. D 76, 081301 (2007)

    2007

  69. [77]

    Johns and S

    L. Johns and S. Rodriguez, arXiv preprint arXiv:2312.10340 (2023)

    2023 arXiv

  70. [78]

    Johns, arXiv preprint arXiv:2402.08896 (2024)

    L. Johns, arXiv preprint arXiv:2402.08896 (2024)

    2024

  71. [79]

    Richers, H

    S. Richers, H. Duan, M.-R. Wu, S. Bhattacharyya, M. Za- izen, M. George, C.-Y. Lin, and Z. Xiong, Phys. Rev. D 106, 043011 (2022), arXiv:2205.06282 [astro-ph.HE]

    2022 arXiv

  72. [80]

    Urquilla and S

    E. Urquilla and S. Richers, Phys. Rev. D 109, 103040 (2024)

    2024

  73. [81]

    Padilla-Gay, H.-H

    I. Padilla-Gay, H.-H. Chen, S. Abbar, M.-R. Wu, and Z. Xiong, arXiv preprint arXiv:2505.11588 (2025)

    2025 arXiv

  74. [82]

    D. F. G. Fiorillo and G. G. Raffelt, arXiv preprint arXiv:2505.20389 (2025)

    2025

  75. [83]

    Froustey, C

    J. Froustey, C. Pitrou, and M. C. Volpe, J. Cosmol. As- tropart. Phys. 2020 (12), 015

    2020

  76. [84]

    Johns, Int

    L. Johns, Int. J. Mod. Phys. A 39, 2450122 (2024)

    2024

  77. [85]

    A. Kost, L. Johns, and H. Duan, Phys. Rev. D 109, 103037 (2024)

    2024

  78. [86]

    H. Duan, G. M. Fuller, and Y.-Z. Qian, Annu. Rev. Nucl. Part. Sci. 60, 569 (2010)

    2010

  79. [87]

    Hannestad, G

    S. Hannestad, G. G. Raffelt, G. Sigl, and Y. Y. Wong, Phys. Rev. D 74, 105010 (2006)

    2006

  80. [88]

    W. D. Heiss, J. Phys. A 45, 444016 (2012)

    2012

  81. [89]

    H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (John Wiley & Sons, 1985)

    1985

  82. [90]

    Abragam and W

    A. Abragam and W. G. Proctor, Phys. Rev. 109, 1441 (1958)

    1958

  83. [91]

    Philippot, Phys

    J. Philippot, Phys. Rev. 133, A471 (1964)

    1964

  84. [92]

    A. G. Redfield, Science 164, 1015 (1969)

    1969

  85. [93]

    E. M. Purcell and R. V. Pound, Phys. Rev. 81, 279 (1951)

    1951

  86. [94]

    Abragam and W

    A. Abragam and W. G. Proctor, Phys. Rev. 106, 160 (1957)

    1957

  87. [95]

    Abragam and M

    A. Abragam and M. Goldman, Rep. Prog. Phys. 41, 395 (1978)

    1978

  88. [96]

    W.-K. Rhim, A. Pines, and J. S. Waugh, Phys. Rev. Lett. 25, 218 (1970)

    1970

  89. [97]

    V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov spectra of turbulence I: Wave turbulence (Springer-Verlag, 1992)

    1992

  90. [98]

    P. H. Diamond, S.-I. Itoh, and K. Itoh, Modern Plasma Physics: Volume 1, Physical Kinetics of Turbulent Plas- mas (Cambridge University Press, 2010)

    2010

  91. [99]

    Abbar, Phys

    S. Abbar, Phys. Rev. D 103, 045014 (2021)

    2021

  92. [100]

    Bhattacharyya, M.-R

    S. Bhattacharyya, M.-R. Wu, and Z. Xiong, arXiv preprint arXiv:2504.11316 (2025)

    2025 arXiv

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