{"id":"a3dc0769-d59d-4a02-8604-99a254ffc83f","arxiv_id":"2504.21734","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The authors use a quasiparticle kinetic-theory model to compute the Thomson, magneto-Thomson, and transverse Thomson coefficients of the quark-gluon plasma, finding strong dependence on baryon chemical potential and magnetic field decay time.","lead":"This paper calculates the Thomson coefficient, which measures heat absorbed or released when an electric current flows through a temperature gradient, for the quark-gluon plasma produced in heavy-ion collisions. It is the first estimate of this coefficient in a time-varying magnetic field, including transverse and magneto versions, with maps of how they depend on collision energy, baryon chemical potential, and magnetic field lifetime.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The magneto-Thomson and transverse Thomson results rest on an imported delta_f expression with a hand-imposed sign rule; Eq. (26) is not derived here, and a wrong sign for H2i/H4i would flip Th_B and Th_N.","rationale":"The reader's weakest assumption identifies exactly the point on which the magnetic-field results depend: Eq. (26) is imported, and the sign information for the Hall terms is lost and then restored by hand. This is not merely a matter of disagreement with other calculations; it is an admitted loss of information in the derivation of the central quantities. If the hand-imposed sign rule is wrong, the new magneto-Thomson and transverse Thomson coefficients change sign or magnitude, so the headline novelty rests on an unverified input. The concrete test is a direct re-derivation from Eq. (22), which would settle whether Eq. (26) and the sign rule are correct. I do not recommend rejecting the paper outright because the zero-field Thomson calculation is internally well motivated and the quasiparticle/RTA framework is standard, but the magnetic-field claims should remain conditional until Eq. (26) is independently derived and the sign issue is resolved. The reader's CONDITIONAL verdict is therefore appropriate, and my stress-test does not move it.","tokens_in":18109,"tokens_out":14428,"duration_ms":148996,"concrete_test":"Independently derive Eq. (26) by substituting the ansatz (25) into Eq. (22) for B(t)=B0 exp(-tau/tau_B), without using the replacement tau_B=omega_i/(q_i B) and without discarding the q_i sign inside H2i and H4i. Then compare the resulting j_x and j_y with Eqs. (28)-(29): does the direct solution reproduce the manual minus/plus sign rule stated after Eq. (33), and does it remain valid at tau_B=3 fm where chi_i is not small? If the direct solution differs in sign or magnitude, recompute Figs. 2-5 with the corrected H2i/H4i; a sign change in Th_N would invalidate the headline claim as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The zero-field Thomson coefficient follows from the standard RTA derivation in Eqs. (8)-(16), but the magnetic-field headline claims are carried entirely by the delta_f_i expression in Eq. (26), which is imported from Ref. [33] rather than derived in this paper. The text immediately after Eq. (33) concedes that H2i and H4i should inherit a sign from the electric charge through chi_i, but that this information vanishes in the approximation, so signs are imposed by hand for the numerical evaluation. No check is shown that this sign rule reproduces a direct solution of the BTE in Eq. (22) with B(t)=B0 exp(-tau/tau_B), particularly for the rapidly decaying fields tau_B=3 fm used in Figs. 2-5. If the sign or magnitude of H2i/H4i is wrong, the Hall-like contributions sigma_H and I_42 in Eqs. (39)-(40) change, and hence S_B, N_B, Th_B, and Th_N in Eqs. (41)-(42) change; the central claim of calculating these coefficients for the first time would then not be supported. The same equations also mix two distinct roles for tau_B: a physical field decay constant (3 or 7 fm) and, as stated after Eq. (33), an inverse cyclotron frequency tau_B=omega_i/(q_i B). This identification is not justified in the manuscript and enters chi_i in every magnetic transport coefficient. The concern is specific to the claimed novelty; the zero-field part of the paper is not affected.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18547,"tokens_out":9769,"duration_ms":91342,"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":[{"comment":"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.","section":"II.B, Eq. (26) and Eq. (33)"},{"comment":"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.","section":"II.B, after Eq. (33)"},{"comment":"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.","section":"II.B, Eq. (42)"},{"comment":"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.","section":"II.C"}],"minor_comments":[{"comment":"The Thomson term should read -Th j · ∇T; the current ordering of the gradient and current is likely a typographical error.","section":"II.A, Eq. (21)"},{"comment":"Write S = I1/(T sigma_el) explicitly rather than as a ratio of fractions for clarity.","section":"II.A, Eq. (13)"},{"comment":"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.","section":"Figs. 2-3"},{"comment":"The choice of magnetic field along the z axis should be stated before the components of the current are written in Eqs. (28)-(29).","section":"II.B, after Eq. (27)"},{"comment":"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.","section":"II.B, after Eq. (33)"},{"comment":"Ref. [64] has a typographical issue in the page range ('1283 822' instead of the expected format).","section":"References"},{"comment":"The MHD mapping between proper time and temperature from Ref. [33] is used without explanation; include the functional relation used in the present analysis.","section":"Sec. III"}],"recommendation":"major_revision","confidential_remarks":"The paper's central novelty is partly derivative: Th_B and Th_N are temperature derivatives of S_B and N_B computed from the same model, and the only new physics input is the magnetic-field delta_f imported from the authors' previous work. If the sign-rule and tau_B issues are resolved, the paper would be publishable as a numerical extension of the existing Seebeck/Nernst studies, but the current version does not yet establish the reliability of the headline coefficients. The authors should also consider softening the abstract's 'for the first time' phrasing in light of the direct relationship to their earlier magneto-Seebeck and Nernst results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nPunchline: this is the first estimate of the Thomson coefficient in QGP, and the zero-field part is a clean, standard calculation. The magneto-Thomson and transverse Thomson numbers, however, rest on an imported delta_f with a hand-imposed sign rule, so I would not take those curves as quantitative predictions until the authors justify or fix that step.\n\nWhat's actually new: applying the first Thomson relation (T dS/dT) to the Seebeck coefficient from their earlier quasiparticle model, and doing the same for the magneto-Seebeck and Nernst coefficients. The transverse Thomson coefficient from the Nernst effect is a sensible idea, and the paper correctly notes that all these coefficients are derivatives of the same model output, so they are not independent benchmarks. The plots are clear, and the authors openly acknowledge the limitations of their magnetic-field treatment.\n\nThe soft spots are real but localized. First, Eq. (26) is taken from Ref. [33], not derived here; the paper never shows it solves Eq. (22) for the exponentially decaying field. Second, the identification tau_B = omega_i/(q_i B) after Eq. (33) conflates the physical decay time with inverse cyclotron frequency; this enters every magnetic coefficient through chi_i and is not justified. Third, the sign-fixing for H2i and H4i, admitted in the text, means the signs and magnitudes of Th_B and Th_N are not robust. These are not fatal for the zero-field Thomson result, but they undermine the headline magnetic claims as they stand. Minor points: alpha_s is fixed at 0.5 and there are no error bars, but that is typical for this kind of model study.\n\nThe math is internally consistent as far as I can tell; the derivations in the zero-field section are standard, and the magnetic section faithfully follows the earlier paper. The citation pattern is fine.\n\nWho is this for? People working on thermoelectric transport in QGP and maybe code developers who want to include Thomson heating in fireball evolution. The paper deserves a serious referee, but I would ask the authors to either derive Eq. (26) properly for the time-dependent case or at least test the sign rule against a direct numerical solution of the BTE. Until then, I would treat the magneto curves as illustrative.\n\nRecommendation: send to peer review, with major revision or a clear caveat.\n\nBest.","headline":"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.","tokens_in":18994,"tokens_out":2288,"would_cite":false,"duration_ms":22243,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Mh","25.75.-q"],"model":"deepseek-v4-flash","headline":"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.","keywords":["Thomson coefficient","quark-gluon plasma","magneto-Thomson coefficient","transverse Thomson coefficient","Nernst effect","relaxation time approximation","quasiparticle model","time-dependent magnetic field"],"falsifier":"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 $Th_N$.","tokens_in":17926,"feed_emoji":"⚡","tokens_out":9040,"duration_ms":84741,"temperature":0.7,"pith_summary":"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.","feed_headline":"Quark-gluon plasma has nonzero Thomson thermoelectric coefficients","feed_subtitle":"Baryon-rich quark matter absorbs or releases heat as current flows; magnetic fields add transverse thermoelectric terms.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the magnetic-field-dependent deviation $\\delta f_i$ (Eq. 26) and the magneto-Seebeck/Nernst formalism this paper extends.","marker":"[33]"},{"why":"Defines the heat current $\\vec{I}$ and the relaxation-time-approximation kinetic theory for charge and heat transport.","marker":"[9]"},{"why":"Provides the RTA solution of the Boltzmann equation and the current and heat-current integrals used in Sec. II A.","marker":"[39]"},{"why":"Gives the quasiparticle model whose equation of state reproduces lattice QCD results.","marker":"[65]"},{"why":"Supplies the thermal-mass expressions for quarks and gluons used in the quasiparticle model.","marker":"[67]"},{"why":"Provides the transverse Thomson coefficient formula $Th_N = T\\,dN_B/dT + 2N_B$ from studies of semimetallic alloys.","marker":"[64]"},{"why":"Motivates the exponential decay form of the time-varying electromagnetic fields in a conducting medium.","marker":"[47]"},{"why":"Parameterizes temperature as a function of baryon chemical potential, enabling the mapping to $\\sqrt{s_{NN}}$.","marker":"[72]"},{"why":"Gives the magnetic-field strength as a function of $\\sqrt{s_{NN}}$ and impact parameter for Au-Au collisions.","marker":"[73]"},{"why":"Supplies the first Thomson relation $Th = T\\,dS/dT$ from energy conservation.","marker":"[31]"}],"fun_headline_variants":["QGP shows nonzero Thomson thermoelectric coefficient","Magnetic fields add transverse Thomson effect in quark-gluon plasma","New magneto-Thomson and transverse Thomson coefficients in QGP","Thomson coefficient of quark-gluon plasma mapped across collision energies","Baryon density flips sign of QGP Thomson coefficient"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["QGP shows nonzero Thomson thermoelectric coefficient","Magnetic fields add transverse Thomson effect in quark-gluon plasma","New magneto-Thomson and transverse Thomson coefficients in QGP","Thomson coefficient of quark-gluon plasma mapped across collision energies","Baryon density flips sign of QGP Thomson coefficient"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00057,"raw_usage":{"total_tokens":2769,"prompt_tokens":1092,"completion_tokens":1677,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":708,"completion_tokens_details":{"reasoning_tokens":1592}},"tokens_in":708,"tokens_out":1677,"duration_ms":13922,"temperature":1.0,"reasoning_tokens":1592,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:56:00.306278+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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 $Th_N$.","supporting_citations":[{"cited_title":"Uchida, M","cited_arxiv_id":null,"evidence_quote":"Supplies the first Thomson relation $Th = T\\,dS/dT$ from energy conservation."},{"cited_title":"Gavin, Nucl","cited_arxiv_id":null,"evidence_quote":"Defines the heat current $\\vec{I}$ and the relaxation-time-approximation kinetic theory for charge and heat transport."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the quasiparticle model whose equation of state reproduces lattice QCD results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the thermal-mass expressions for quarks and gluons used in the quasiparticle model."},{"cited_title":"Alasli et","cited_arxiv_id":null,"evidence_quote":"Provides the transverse Thomson coefficient formula $Th_N = T\\,dN_B/dT + 2N_B$ from studies of semimetallic alloys."},{"cited_title":"Satow, Phys","cited_arxiv_id":null,"evidence_quote":"Motivates the exponential decay form of the time-varying electromagnetic fields in a conducting medium."}],"review_version":1}