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REVIEW 4 major objections 7 minor 78 references

Thermoelectric Thomson coefficient of quark-gluon plasma in the presence of a time-varying magnetic field

T0 review · 4 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper claims that the quark-gluon plasma has nonzero Thomson, magneto-Thomson, and transverse Thomson coefficients, and offers the first calculation of the two magnetic-field-induced Thomson coefficients from kinetic theory.

desk verdict First QGP Thomson calculation, but the magneto results rely on an imported, sign-fixed delta_f and a questionable tau_B identification; zero-field part is fine. read the letter →

arxiv 2504.21734 v2 pith:M7FWRJFH submitted 2025-04-30 hep-ph hep-exhep-thnucl-exnucl-th

Kamaljeet Singh , Raghunath Sahoo This is my paper · ORCID
classification hep-phhep-exhep-thnucl-exnucl-th PACS 12.38.Mh25.75.-q
keywords Thomsoncoefficientquark-gluonplasmamagneto-ThomsontransverseNernsteffectrelaxationtimeapproximationquasiparticlemodeltime-dependentmagneticfield
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

This paper claims that a quark-gluon plasma (QGP) is not just electrically conducting but thermoelectric: a temperature gradient in baryon-rich QGP drives an electric current, and because the Seebeck coefficient depends on temperature, the medium continuously absorbs or releases heat through the Thomson effect. The central new results are the first calculations of the magneto-Thomson coefficient and the transverse Thomson coefficient, which appear only when a magnetic field is present, plus a recalculation of the ordinary Thomson coefficient. The authors solve the Boltzmann equation in the relaxation time approximation with an exponentially decaying magnetic field, use a quasiparticle model matched to lattice QCD thermodynamics, and find that the magnetic field lowers the magneto-Thomson coefficient, while the transverse coefficient is driven by the Nernst effect and can be large and negative at low temperatures. These coefficients modify the heat and charge currents and, if correct, change how the QGP cools in heavy-ion collisions.

What carries the argument

The load-bearing objects are the first Thomson relation $Th = T\,dS/dT$, which converts the temperature dependence of the Seebeck coefficient into the heat absorbed or released per unit current, and its magnetic-field counterpart, the 2x2 matrix coupling the electric field components $(E_x,E_y)$ to $(\partial_x T,\partial_y T)$ with entries $S_B$ and $N_B$. The explicit computation is carried by four momentum integrals $H_{1i}$ through $H_{4i}$: Ohmic-like and Hall-like charge and heat integrals over quark distribution functions, together with an ansatz for the non-equilibrium distribution function that includes time-derivative and cross-product terms of the electric field, magnetic field, and temperature gradient. A quasiparticle model with thermal masses matched to lattice QCD supplies the equation of state, and the relaxation time is taken momentum-independent. The transverse coefficient exists only because the Nernst coefficient $N_B$ is nonzero, so it vanishes when the magnetic field is switched off.

What would settle it

Compute the deviation $\delta f_i$ (Eq. 26) and the integrals $H_{2i}$, $H_{4i}$ without replacing the field decay time by $\omega_i/(q_i B)$; if the explicit charge signs in $\chi_i$ are retained, the hand-imposed signs can be checked, and any flip in the signs of $S_B$ or $N_B$ would reverse the predicted signs of $Th_B$ and $Th_N$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the QGP possesses a nonzero Thomson coefficient $Th = T\,dS/dT$, inherited from the temperature dependence of its Seebeck coefficient $S$, and that in the presence of a time-dependent magnetic field two additional higher-order coefficients appear: the magneto-Thomson coefficient $Th_B = T\,dS_B/dT$ built from the magneto-Seebeck coefficient, and the transverse Thomson coefficient $Th_N = T\,dN_B/dT + 2N_B$ built from the normalized Nernst coefficient. For low baryon chemical potential $\mu_B$, $Th$ is positive and grows with temperature; for higher $\mu_B$ it is negative. A magnetic field with $eB_0 = 5\,m_\pi^2$ suppresses $Th_B$ relative to $Th$, more strongly for a faster field decay, and $Th_N$ is negative at low temperature and approaches zero at high temperature. When the results are mapped onto collision energy, $Th_B$ crosses from negative to positive near $\sqrt{s_{NN}} \approx 20$ GeV, while $Th_N$ stays negative and approaches zero at 200 GeV.

Load-bearing premise

The transverse and magneto-Thomson results rest on the magnetic-field part of the distribution function; the derivation erases the sign of the electric charge from two of the key integrals, and the authors put the signs back by hand.

Editorial extensions

If this is right

  • The heat current in QGP is modified to include the Thomson term, so hydrodynamical and transport models that evolve the cooling medium should add $Th\,\vec{j}\cdot\vec{\nabla}T$ to the local energy balance.
  • In peripheral collisions the magnetic field generates a transverse thermoelectric response, so both $Th_B$ and $Th_N$ should enter magnetohydrodynamic simulations of the medium's temperature profile.
  • Because $Th$ changes sign with baryon chemical potential, baryon-rich matter at low $\sqrt{s_{NN}}$ releases heat while high-energy matter absorbs it, giving a beam-energy-dependent correction to QGP cooling.
  • The nonzero Seebeck coefficient reduces the effective thermal conductivity from $\kappa_0$ to $\kappa_0 - T\sigma_{el}S^2$, so thermoelectric effects partially counteract heat conduction.

Reading between the lines

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

  • If the sign-fixing in $H_{2i}$ and $H_{4i}$ is wrong, the Hall and Nernst contributions reverse, so the numerical signs of $Th_B$ and $Th_N$ are the most fragile part of the result.
  • The paper's field-dependent distribution function is taken from an earlier reference and assumes a slowly varying field; a solution valid for rapid decay would test whether Eq. (26) actually follows from the ansatz Eq. (25).
  • The paper explicitly sets aside Landau quantization of quark energies; restoring it could shift the magneto-transport coefficients at early times, when $eB$ is at its peak.
  • Because all coefficients diverge at $\mu_B=0$, the physically testable regime is baryon-rich matter, which is why the predicted sign change of $Th_B$ near $\sqrt{s_{NN}}\approx 20$ GeV is the cleanest place to look.
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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

4 major / 7 minor

Summary. This paper uses the relaxation-time approximation to the Boltzmann equation to compute the Thomson coefficient of the quark-gluon plasma within a quasiparticle model. In the zero-field case, the Seebeck coefficient is derived from the electric and heat currents, and the Thomson coefficient is obtained through the first Thomson relation, Th = T dS/dT. For the case of a time-dependent magnetic field of exponential form, the authors import a delta_f expression from their earlier work, define integrals H1i-H4i, and construct the magneto-Seebeck, Nernst, magneto-Thomson, and transverse Thomson coefficients. Numerical results are presented as functions of temperature, baryon chemical potential, and collision energy for decay parameters tau_B = 3 and 7 fm. The central claims are the first calculation of the magneto-Thomson and transverse Thomson coefficients in QGP.

Significance. If the magnetic-field part were rigorously derived, the paper would provide the first estimates of the magneto-Thomson and transverse Thomson coefficients for QGP, extending earlier studies of Seebeck and Nernst coefficients. The zero-field Thomson coefficient is a straightforward temperature derivative of S and is not conceptually new, but the numerical results in the quasiparticle model are useful as predictions. The magnetic-field results, however, depend on an imported distribution function and a manually fixed sign convention for the Hall integrals, which limits their reliability until verified. The paper is clearly written and the zero-field derivation is sound.

major comments (4)
  1. [II.B, Eq. (26) and Eq. (33)] The entire magnetic-field calculation rests on the delta_f expression in Eq. (26), which is not derived in this paper but imported from Ref. [33]. Immediately after Eq. (33), the authors note that H2i and H4i should inherit a sign from the electric charge through chi_i, but this information 'vanishes due to the approximation,' and signs are imposed by hand. Since S_B, N_B, Th_B, and Th_N in Eqs. (39)-(42) depend on these integrals, an incorrect sign rule would flip the signs of the headline magneto-Thomson and transverse Thomson coefficients. To support the claim of calculating these coefficients, the paper must derive Eq. (26) from the BTE with the time-dependent field of Eq. (23) or provide a direct test of the sign rule, e.g., by solving Eq. (22) numerically for a simple relaxation-time model.
  2. [II.B, after Eq. (33)] The manuscript identifies the physical decay time tau_B of the magnetic field profile (23) with the inverse cyclotron frequency tau_B = omega_i/(q_i B), while simultaneously using tau_B = 3 and 7 fm as decay constants in Figs. 2-5. These two time scales are conceptually different: the slowly-varying-field limit requires tau_B^decay >> omega_i/(q_i B), not equality. Furthermore, since B(t) decays, it is unclear whether chi_i is evaluated with the initial field, the instantaneous field from the MHD mapping, or a time-averaged value. This ambiguity propagates into every magnetic transport coefficient and should be resolved by either justifying the identification or solving the BTE with explicit time dependence.
  3. [II.B, Eq. (42)] The transverse Thomson coefficient Th_N = T dN_B/dT + 2 N_B is taken from Ref. [64] without derivation. Given that Th_N is one of the two new quantities claimed in the abstract, the paper should show how this relation follows from the energy balance equation or the Onsager framework in the presence of a magnetic field, or clearly state that it is a phenomenological definition whose applicability to QGP is assumed. As written, the calculation of Th_N is an application of a condensed-matter formula rather than a derivation.
  4. [II.C] The numerical calculations are not fully reproducible because the bare quark masses m_i0 in the dispersion relation m_i^2 = m_i0^2 + sqrt(2) m_i0 m_iT + m_iT^2 are never specified. The values of m_i0 (or the statement that they are set to zero) must be provided, together with any other QPM parameters used to produce Figs. 1-5.
minor comments (7)
  1. [II.A, Eq. (21)] The Thomson term should read -Th j · ∇T; the current ordering of the gradient and current is likely a typographical error.
  2. [II.A, Eq. (13)] Write S = I1/(T sigma_el) explicitly rather than as a ratio of fractions for clarity.
  3. [Figs. 2-3] Use eB0 consistently with the text; the figure labels read 'eB = 5.0 m_pi^2' instead of the initial-field notation used in the text.
  4. [II.B, after Eq. (27)] The choice of magnetic field along the z axis should be stated before the components of the current are written in Eqs. (28)-(29).
  5. [II.B, after Eq. (33)] The sentence 'we use the minus (plus) sign in H2i and H4i for negatively (positively) charged particles and antiparticles' is ambiguous; it should specify which sign is applied to quarks and antiquarks of each charge separately.
  6. [References] Ref. [64] has a typographical issue in the page range ('1283 822' instead of the expected format).
  7. [Sec. III] The MHD mapping between proper time and temperature from Ref. [33] is used without explanation; include the functional relation used in the present analysis.

Circularity Check

1 steps flagged · score 4.0 of 10

The zero-field Thomson derivation is self-contained, but the headline magnetic coefficients are carried by an imported self-cited δf expression whose charge-sign dependence is lost and then re-imposed by hand.

  1. self citation load bearing [Section II B, Eq. (26) and following Eqs. (30)-(33), (39)-(42)]
    "After getting the expressions for αj’s, the simplified form of δfi is (see Appendix of Ref. [33]): ... Here, it is important to note that the expressions are obtained in the limit of a slowly varying magnetic field, for which we approximated the decay parameter as the inverse of cyclotron frequency, ı.e., τB = ωi/qiB. Furthermore, H2i and H4i should have explicit sign dependency from the electric charge of the particle due to χi in the numerator. However, this information vanishes due to the approximation."

    The B-field deviation δfi in Eq. (26) is not derived in this paper but taken from the authors' own Ref. [33]. All magnetic transport quantities — σH, I42, SB, NB, and then ThB, ThN through Eqs. (39)-(42) — are constructed from the H2i/H4i integrals that inherit Eq. (26). Thus the claimed new magnetic coefficients reduce to a self-citation rather than to an in-paper solution of the BTE, since the αj coefficients are not shown here. The text also admits that the physical charge-sign information in H2i and H4i vanishes and is re-imposed manually; the signs of ThB and ThN are therefore inputs, not derived predictions. The zero-field Thomson coefficient is unaffected, but the central magnetic results are load-bearing on the imported expression and hand-fixed sign rule.

full rationale

The paper contains a genuine self-contained derivation for the zero-field Thomson coefficient: Eqs. (1)-(16) define the equilibrium distribution, solve the RTA Boltzmann equation for δfi, obtain the Seebeck coefficient S as a ratio of thermal and electrical integrals, and then use the standard first Thomson relation Th = T dS/dT. No data are fitted and the Thomson coefficient is not renamed as an independent prediction; it is a thermodynamic derivative of the computed S, which is an acceptable definitional relation rather than a circular step. The magnetic part is different. The derivation of the magnetic distribution function is not reproduced: Eq. (26) is explicitly delegated to the authors' earlier Ref. [33], a paper with overlapping authorship. All later magnetic coefficients, including the headline magneto-Thomson and transverse Thomson coefficients, are functions of H2i and H4i taken from this imported formula. The paper itself states that the electric-charge sign dependence of these integrals disappears in the approximation and that signs are put in by hand for numerics. Consequently, if the sign rule or the imported δfi were different, SB, NB, ThB, and ThN would change, including their signs. This makes the central magnetic claims dependent on a self-citation chain plus a manual sign choice, rather than on an independent in-paper derivation or external benchmark. However, the zero-field Thomson calculation is honest, standard, and self-contained, so the circularity is only partial and concentrated in the magnetic extension.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The calculation depends on the QPM/RTA framework and on coefficients adopted from prior work by the same group. No external benchmark or direct measurement anchors the numerical values, and the sign-fixing step in the magnetic sector is unverified.

free parameters (5)
  • Strong coupling alpha_s = 0.5 = 0.5
    Section II C states 'the value of the strong coupling constant is taken to be fixed at alpha_s = 0.5' for numerical estimation, although Eq. (45) defines a running alpha_s(T, mu_B, eB). The Thomson coefficients scale with relaxation time and thermal masses, both sensitive to alpha_s; no uncertainty or sensitivity scan is given.
  • QCD scale-fixing parameter Lambda_T = 0.115 GeV
    Used in Eq. (45) for the magnetic-field-dependent running coupling; adopted from the QPM literature, not derived here, and no sensitivity is shown.
  • Relaxation-time normalization coefficients = 5.1 and 0.12(2N_f+1)
    Eq. (46) from Hosoya and Kajantie; the momentum-independent tau_R enters every transport integral linearly, so its normalization directly scales the coefficients. It is taken from literature rather than computed or calibrated here.
  • Bare quark masses m_i0 = not specified
    The thermal mass formula in Sec. II C includes bare masses m_i0 via m_i^2 = m_i0^2 + sqrt(2) m_i0 m_iT + m_iT^2, but the numerical values used are not stated; this is an unspecified input to the numerical evaluation.
  • Initial magnetic field eB0 and decay times tau_B = 5 m_pi^2, 3 and 7 fm
    Chosen as representative values for Figs. 2 and 3; in the sqrt(s_NN) scan Eq. (48) sets eB0 around 3 m_pi^2 for Au-Au at 200 GeV. These choices control the magneto and transverse coefficients, and no uncertainty is given.
assumptions (6)
  • domain assumption The QGP is describable by a Boltzmann transport equation with on-shell quasi-particles and a momentum-independent relaxation time (RTA).
    Invoked in Sec. II A for Eq. (2) and used for all currents; strongly coupled QGP may not satisfy this quasiparticle description.
  • domain assumption The quasiparticle model with thermal masses and a bag constant reproduces the lattice QCD equation of state.
    Sec. II C adopts the Gorenstein-Yang QPM; the transport coefficients inherit its thermodynamic input.
  • domain assumption The first Thomson relation Th = T dS/dT and the transverse relation Th_N = T dN_B/dT + 2 N_B remain valid for a multi-component relativistic plasma with baryon-charge transport.
    Eqs. (16), (41), and (42) are taken from condensed-matter thermoelectricity; the paper does not derive them within relativistic kinetic theory.
  • domain assumption Baryon number is the conserved charge and mu_B is non-zero; at mu_B = 0 the thermoelectric coefficients diverge.
    The summary states 'a non-zero baryon chemical potential is necessary. Otherwise, thermoelectric coefficients diverge at zero baryon chemical potential'; this limits applicability at LHC-like conditions.
  • ad hoc to paper The magnetic field is slowly varying with decay time identified as tau_B = omega_i/(q_i B), and Landau quantization is neglected.
    Sec. II B states the slowly-varying limit and Sec. IV notes Landau quantization is not considered; this is needed for Eq. (26) and chi_i.
  • ad hoc to paper The sign of the Hall-type integrals H2i and H4i can be assigned by hand after the approximation removes the charge-sign information.
    After Eq. (33), the authors state the sign dependency vanishes and insert signs for numerical estimation; this is an unproved handling step.

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Pith. "Pith review of Thermoelectric Thomson coefficient of quark-gluon plasma in the presence of a time-varying magnetic field." pith.science (2026). https://pith.science/paper/M7FWRJFH

@misc{pith2026250421734,
  author       = {Pith},
  title        = {Pith review of: Thermoelectric Thomson coefficient of quark-gluon plasma in the presence of a time-varying magnetic field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M7FWRJFH}},
  note         = {Machine review of arXiv:2504.21734}
}
read the original abstract

Heavy-ion collision experiments such as the Large Hadron Collider and the Relativistic Heavy Ion Collider offer a unique platform to study several key properties of the quark-gluon plasma (QGP), a deconfined state of strongly interacting matter. Quarks, being the electrically charged particles, can induce an electric current in the medium in response to the temperature gradients. Hence, the QGP medium can behave like a thermoelectric medium. The thermoelectric coefficients, such as the Seebeck and Thomson coefficients, can help us to understand the intricate transport phenomenon of the medium. In peripheral collisions, the intense, transient, and time-dependent magnetic field created due to spectator protons significantly influences the thermoelectric properties of the QGP medium, affecting the charge and heat transport. This work uses the quasi-particle model to calculate the Thomson coefficient in QGP. The Thomson effect, describing the continuous heating or cooling of the charge-carrying medium in the presence of temperature gradients, remains largely unexplored in QGP. The Seebeck effect, which relates temperature gradients to induced electric fields, has been widely studied in the literature. For the first time, we calculate the magneto-Thomson and transverse Thomson coefficients. We have studied their dependence on temperature, baryon chemical potential, center of mass energy, and time-dependent magnetic field with different decay parameters. The transverse Thomson effect originates due to the presence of the Nernst effect in the presence of a magnetic field. Our results provide new insights into the higher-order thermoelectric transport properties of the QGP medium in the context of heavy-ion collisions.

Figures

Figures reproduced from arXiv: 2504.21734 by the authors.

Figure 1
Figure 1. FIG. 1: Left: Seebeck coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Left: magneto-Seebeck coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Left: normalized Nernst coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Left: magneto-Seebeck coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Left: normalized Nernst coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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