{"id":"b609266a-5b92-4ef4-b82b-16f8fad2f3d3","arxiv_id":"2507.16787","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A detector in rotating BTZ spacetime thermalizes faster when heating than when cooling, but the effect traces to the two baths having different temperatures.","lead":"The paper derives the full open quantum dynamics of a detector orbiting a rotating BTZ black hole and applies quantum thermodynamic laws to its thermalization. It claims the detector heats faster than it cools, an effect it likens to the quantum Mpemba effect, though the comparison uses different local bath temperatures.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Heating/cooling asymmetry is not intrinsic: the protocol compares two different baths, and the claimed Mpemba-like effect is an artifact of fixing different T_H and T_C rather than a property of the dynamics.","rationale":"I agree with the reader's weakest-assumption identification and with the REJECT verdict, so I can give my reasoning succinctly: (1) The formal framework is sound: the UDW master equation has a unique stationary state and the relaxation rate is independent of the initial Bloch vector (Eq. 2.14). (2) The protocol in Section 4 compares two detectors at distinct radial positions, i.e., two different baths with T_H and T_C, so the comparison does not establish an intrinsic asymmetry of a given thermalization dynamics. (3) The paper's own insets show that the instantaneous quantum speed v_Q crosses over, which is why the authors shift to the 'degree of completion' R_{t/T}; but R_{t/T} depends on the arbitrary horizon T and cannot certify a fundamental heating/cooling asymmetry. (4) The correct physical statement is the weaker, well-known observation that a hotter bath causes faster relaxation, not a quantum Mpemba effect. The claim of 'intrinsic asymmetry' is therefore load-bearing and false as an interpretation. No independent evidence (machine-checked proof, reproducible code, parameter-free derivation) saves the central claim, so the reader's REJECT verdict stands unchanged. I would add a note that the concrete test can be done analytically since Eqs. 2.14-2.15 and 4.6-4.8 are closed form.","tokens_in":32049,"tokens_out":1664,"duration_ms":16550,"concrete_test":"Run the proposed heating/cooling protocol with both detectors in the same bath: simulate two UDW detectors at the same radial position (same T_KMS), one initialized in a Gibbs state at T_C and the other in a Gibbs state at T_H, and compare F_heating(t) and F_cooling(t) using Eqs. 4.6 and 4.8 with identical C(omega). Because the relaxation rate in Eq. 2.14 is independent of initial state, one should find F_heating(t) = F_cooling(t) exactly (up to numerical noise). This would isolate the bath-temperature difference as the source of the asymmetry and settle whether the claimed effect is intrinsic.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim (Section 5: 'the heating protocol for a UDW detector is always faster than the cooling one') is unsupported by the protocol in Section 4. The Lindblad relaxation rate depends only on the bath response functions C(omega), C(-omega), C(0) (Eqs. 2.11, 2.14), which are fixed by the field state at the detector's location, not on the detector's initial state. Both detectors undergo the same Markovian relaxation toward their local KMS state; if both were placed in the same bath at the same temperature, heating from T_C and cooling from T_H would be time-reversed images with identical speed (the Bloch equation is linear and the decay rate is state-independent). The reported asymmetry therefore encodes the chosen difference between the two local temperatures T_H and T_C, not an intrinsic heating-vs-cooling asymmetry of the thermalization dynamics. Moreover, Fig. 12's inset itself shows that v_Q(cooling) exceeds v_Q(heating) at later times; the paper responds by replacing speed with the 'quantum degree of completion' R_{t/T} (Eq. 4.9), but this ratio depends on the arbitrary end time T, so it does not establish a protocol-independent asymmetry either. The abstract's phrase 'intrinsic asymmetry' is thus a misinterpretation of the numerics, a load-bearing interpretive error even though the technical framework may be internally consistent.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the thermalization of an Unruh-DeWitt detector co-rotating outside a rotating BTZ black hole. Starting from a Markovian master equation, the authors analytically compute the detector's response to a massless scalar field with Neumann, transparent, and Dirichlet boundary conditions, and use the resulting Kossakowski coefficients to analyze the detector's quantum relative entropy, heat/coherence/work decomposition, entropy production, and quantum Fisher information. The advertised main result is an \"intrinsic asymmetry\" between heating and cooling: a detector heating from T_C to T_H is claimed to thermalize faster than a detector cooling from T_H to T_C, in analogy with the quantum Mpemba effect. The paper also examines how black hole angular momentum and boundary conditions affect these thermodynamic quantities.","tokens_in":32360,"tokens_out":13115,"duration_ms":138298,"significance":"If the asymmetry claim were correct, it would connect black hole rotation to a genuine quantum-thermodynamic effect and would be of interest to the quantum-information and gravitational communities. The paper has real technical merit: the analytic response function in Eq. (2.39) and its derivation in Appendix A, the explicit Bloch solution (2.14), and the closed-form thermodynamic quantities in Section 3 are presented without fitted parameters and appear internally consistent. However, the central interpretive claim is not supported by the protocol or the measures used, as detailed below. The useful parts of the paper are therefore the thermodynamic-law analysis, not the Mpemba analogy.","major_comments":[{"comment":"The central claim of an intrinsic heating/cooling asymmetry is not supported. For a fixed bath, the Bloch solution (2.14) gives n_z(t) = -γ ± δ e^{-2g^2 γ_+ t} for symmetric heating and cooling initial conditions, i.e., the two evolutions are mirror images with the same relaxation rate. The fidelity (4.4) is a nonlinear function of l(t), so F_heating ≥ F_cooling can hold even when the underlying state-space distance decays identically; the inequality reflects a property of the measure, not of the dynamics. The inset of Fig. 12 shows v_Q(cooling) exceeding v_Q(heating) at later times, which directly undermines the speed claim, and the replacement of speed by R_{t/T} in Eq. (4.9) depends on an arbitrary end time T and therefore does not establish a protocol-independent asymmetry. The abstract's \"intrinsic asymmetry\" and Section 5's statement that \"the heating protocol for a UDW detector is always faster than the cooling one\" are accordingly overstatements.","section":"Section 4, Eq. (2.14), Fig. 12"},{"comment":"The heating and cooling processes are run in different baths at local temperatures T_H and T_C. Because the Kossakowski coefficients in Eqs. (2.11) and (2.42) depend on the detector's local temperature, the comparison conflates the temperature dependence of γ_+ with any intrinsic heating/cooling asymmetry. To isolate an intrinsic effect, the authors would need to compare heating and cooling in the same bath at fixed T, with initial states at T_C < T and T_H > T chosen symmetrically around T; the present design does not control for this.","section":"Section 4 protocol (Fig. 11)"},{"comment":"The analogy to the quantum Mpemba effect is not justified. The quantum Mpemba effect refers to a state that starts farther from equilibrium relaxing faster than a closer one in the same environment, or to a symmetry-breaking initial condition relaxing faster than a symmetric one. Here the comparison is between different environments at different temperatures, and no ordering of relaxation rates independent of the chosen information-geometric measure is demonstrated. The data show at most that F_heating(t) ≥ F_cooling(t) for the specific temperature pair and boundary conditions used.","section":"Abstract and Section 4"}],"minor_comments":[{"comment":"The word \"thermolization\" should be \"thermalization\" in both places.","section":"Abstract and Section 5"},{"comment":"The sentence \"at later times, the heating velocity surpasses cooling\" appears to be a typo; the surrounding discussion and the insets of Fig. 14 suggest it should read \"is surpassed by cooling.\"","section":"Section 4, text near Fig. 12"},{"comment":"The reference \"Fig.??\" is unresolved and should be replaced with the actual figure number.","section":"Appendix A"},{"comment":"There are several typos, including \"in genenral\" and \"repectively,\" which should be corrected.","section":"Section 3.3"}],"recommendation":"reject","confidential_remarks":"The technical apparatus is largely correct and potentially useful, but the headline result is not established. If the authors wish to resubmit, they should reframe the paper around the thermodynamic-law analysis and either remove or rigorously redefine the asymmetry claim; as it stands, the central claim is an artifact of the chosen protocol and measures."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The technical body of this paper is in good shape, but the headline claim does not hold up. The authors take the known response function for a co-rotating UDW detector in rotating BTZ (Hodgkinson and Louko), feed it through the standard Lindblad machinery, and compute a full set of thermodynamic quantities: quantum relative entropy, heat/coherence decomposition, entropy production, quantum Fisher information. All of that is competently done. The appendices check out, nothing is fitted, and the boundary-condition comparison (Dirichlet giving a much slower thermalization) is consistent with what was known before. For a reader working on open quantum systems in 2+1 black holes, this is a useful reference for the formulas and the numerics.\n\nThe problem is the central interpretive claim in the abstract and Section 5: that heating is intrinsically faster than cooling, with a quantum-Mpemba-like asymmetry. The protocol in Section 4 compares two detectors in two different baths. The closer detector heats in a hot bath at T_H; the farther detector cools in a cold bath at T_C. But the Bloch solution (2.14) shows the relaxation rate depends only on the bath coefficients gamma_+, not on the initial state. For a fixed bath, heating from below and cooling from above are time-reversed and equally fast. So the reported asymmetry is driven by the hand-picked difference between T_H and T_C, not by any property of the thermalization dynamics. That is a load-bearing misinterpretation: the abstract and conclusions are selling an effect that the setup does not actually demonstrate.\n\nThe paper itself notices the trouble: in Fig. 12's inset, the cooling speed exceeds the heating speed at later times. The response is to replace speed with the 'quantum degree of completion' R_{t/T}, but that ratio depends on an arbitrary end time T and does not establish a protocol-independent asymmetry. The analogy to the quantum Mpemba effect is also misleading: quantum Mpemba is about initial-state-dependent relaxation rates, and here the rate is state-independent.\n\nThe rest of the paper remains credible. The thermodynamic laws, the information-geometry identities, and the BTZ numerics are a reasonable application of existing methods. The flaw is interpretive, not computational.\n\nWho gets value: researchers who want the explicit Kossakowski coefficients, QFI expressions, and boundary-condition behavior for UDW detectors in rotating BTZ. They should not cite the heating-cooling asymmetry as an intrinsic effect.\n\nRecommendation: send to peer review. A competent referee will catch the interpretive error, but the paper is otherwise substantial enough to deserve a chance at revision. If the authors reframe the asymmetry as a temperature-profile effect, or drop the Mpemba claim, the technical content is publishable.","headline":"Solid thermodynamics application to BTZ detectors, but the headline heating/cooling asymmetry is an artifact of comparing two different baths, not an intrinsic effect.","tokens_in":32879,"tokens_out":2872,"would_cite":false,"duration_ms":36842,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A detector co-rotating with a BTZ black hole heats faster than it cools.","keywords":["Unruh-DeWitt detector","BTZ black hole","quantum thermodynamics","quantum Mpemba effect","open quantum systems","quantum Fisher information","thermalization asymmetry","Kossakowski coefficients"],"falsifier":"Set both detectors in a single bath at one KMS temperature, initialize them symmetrically around the thermal state with equal angular displacement, and compute the fidelity and degree of completion; since the paper's Bloch solution gives both states the same relaxation rate, equal completion curves in this setup would falsify the claim that heating is intrinsically faster than cooling.","tokens_in":1808,"feed_emoji":"🕳️","tokens_out":4390,"duration_ms":113282,"temperature":0.7,"pith_summary":"The paper derives the full open-quantum-system dynamics of an Unruh-DeWitt detector co-rotating with a BTZ black hole, then treats the resulting relaxation as a quantum thermodynamic process. Its central claim is that approach to equilibrium is direction-dependent: a detector heating toward the locally perceived KMS temperature is always faster than a detector cooling across the same temperature interval, an asymmetry the authors liken to the quantum Mpemba effect. Black hole angular momentum changes how large this heating/cooling gap is but does not reverse it. The same calculation also shows that the choice of boundary conditions for the scalar field at infinity suppresses the oscillations in the thermodynamic quantities under Dirichlet conditions and stretches the thermalization timescale far beyond Neumann or transparent conditions.","feed_headline":"Detector heats faster than it cools around a rotating black hole","feed_subtitle":"Open-quantum-system analysis of BTZ spacetime finds a spin-dependent heating/cooling gap at every finite time.","key_machinery":"The engine of the calculation is the UDW detector treated as a two-level open system whose dissipator is fixed by the Wightman function of a massless conformally coupled scalar in BTZ spacetime. The load-bearing object is the detector response $C(\\omega)$, analytically evaluated by the method of images as a sum over associated Legendre functions for Neumann, transparent, and Dirichlet boundary conditions, satisfying the KMS condition $C(\\omega)=e^{\\beta\\omega}C(-\\omega)$. From it come the Kossakowski coefficients $\\gamma_\\pm$ and $\\gamma_0$ that set the relaxation rates $2g^2(\\gamma_+ + \\gamma_0)$ and $2g^2\\gamma_+$ in the Bloch solution; the asymmetry is then quantified by the Uhlmann fidelity to the final Gibbs state and by the quantum degree of completion $R_{t/T}$, the ratio of path lengths in quantum state space.","core_discovery":"On the paper's own terms: for a two-level UDW detector on a circular co-rotating orbit outside a rotating BTZ black hole, thermalization is not time-reversal symmetric. Using the analytical response function $C(\\omega)$ of the detector to a massless scalar field, the authors solve the GKSL master equation and obtain the full Bloch-vector trajectory, then verify three quantum thermodynamic laws: a zeroth law stated as vanishing quantum relative entropy to the thermal state, a first law splitting internal-energy change into heat, coherence, and (for driven detectors) work, and a second law with nonnegative entropy production. Comparing a detector heating from a lower Gibbs temperature $T_C$ to the local KMS temperature $T_H$ with one cooling from $T_H$ to $T_C$, they find $F_{\\mathrm{heating}}(t) \\geq F_{\\mathrm{cooling}}(t)$ for all finite times and a quantum degree of completion that is always larger for heating, and they show black hole spin modulates the magnitude of this asymmetry.","pith_inferences":["Beyond the paper: the reported asymmetry is a comparison between two different local baths. The heating detector sits in a region with local temperature $T_H$ and the cooling detector in a region with $T_C$, so the two trajectories have different Kossakowski coefficients; the same Bloch equation run at a single common temperature would not exhibit this direction-dependent effect.","Beyond the paper: 'heating faster than cooling' is measured by fidelity and path-completion, not by instantaneous speed. The paper's own insets show the cooling speed can exceed the heating speed at late times, so the claim should be read as path-integrated progress toward equilibrium, not as a statement about instantaneous velocities.","Beyond the paper: the same machinery could be applied to higher odd-dimensional analogs of the Unruh effect, where the statistics-inversion feature the authors note for BTZ might flip or suppress the asymmetry, giving a clean test of whether the effect is specific to 2+1 dimensions."],"forward_implications":["A co-rotating UDW detector outside a BTZ black hole approaches its local equilibrium along asymmetric paths: at every finite time, the fidelity to the thermal state is larger for heating than for cooling.","The black hole's angular momentum affects the size of the heating/cooling asymmetry, but the dominance of heating over cooling is preserved.","Boundary conditions at infinity matter thermodynamically: Dirichlet conditions make the entire thermalization process much slower than Neumann or transparent conditions, and they suppress the oscillatory dependence of thermodynamic quantities on angular momentum.","The quantum First Law becomes three-way bookkeeping: internal-energy change splits into heat, coherence, and work, and in the standard fixed-gap detector the heat and coherence rates trade off while work vanishes.","The quantum Second Law holds through a nonnegative entropy production rate even though the von Neumann entropy itself can temporarily decrease, because entropy flows out to the scalar field."],"supporting_citations":[{"why":"Supplies the open-quantum-systems framework, including the GKSL master equation used to derive the detector's complete dynamics.","marker":"[16]"},{"why":"Provides the analytic response of UDW detectors on BTZ spacetime, including the boundary-condition dependence of transition rates that this work extends.","marker":"[55]"},{"why":"Gives the two-atom Kossakowski-coefficient decomposition used to write the Lindblad dissipator for the detector.","marker":"[47]"},{"why":"Introduces the BTZ black hole geometry that the whole calculation takes as its spacetime.","marker":"[32]"},{"why":"Provides the rotating BTZ metric and the mass/angular-momentum parameterization used throughout the paper.","marker":"[33]"},{"why":"Reports the analogous heating/cooling asymmetry in nonequilibrium systems that the paper claims to find in BTZ spacetime.","marker":"[37]"},{"why":"Defines the quantum Mpemba effect to which the paper likens its heating/cooling asymmetry.","marker":"[40]"},{"why":"Supplies the information-geometry tools (fidelity, quantum speed, degree of completion) used to quantify the asymmetry.","marker":"[39]"},{"why":"Gives the relative-entropy formulation of thermalization in Schwarzschild spacetime that precedes the paper's quantum Zeroth Law.","marker":"[25]"},{"why":"Shows Fisher information as a probe of BTZ spacetime, the precedent for using quantum Fisher information in this setting.","marker":"[30]"}],"fun_headline_variants":["Hotter faster: BTZ black hole heats detectors quicker than it cools","Black hole spin skews detector heating: warms faster than it cools","Quantum Mpemba effect seen as BTZ black hole heats detector faster","Rotating BTZ black hole makes detector heat up faster than cool down"],"cache_read_input_tokens":35072,"weakest_assumption_plain":"The comparison protocol assumes that placing one detector in a hotter local bath and one in a colder local bath, then comparing their relaxation curves, reveals an intrinsic property of the thermalization dynamics rather than simply reflecting the hand-picked difference between the two bath temperatures.","fun_headline_variants_meta":{"raw":{"variants":["Hotter faster: BTZ black hole heats detectors quicker than it cools","Black hole spin skews detector heating: warms faster than it cools","Quantum Mpemba effect seen as BTZ black hole heats detector faster","Rotating BTZ black hole makes detector heat up faster than cool down"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000696,"raw_usage":{"total_tokens":3141,"prompt_tokens":937,"completion_tokens":2204,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":2125}},"tokens_in":553,"tokens_out":2204,"duration_ms":15693,"temperature":1.0,"reasoning_tokens":2125,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:03:05.774922+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Set both detectors in a single bath at one KMS temperature, initialize them symmetrically around the thermal state with equal angular displacement, and compute the fidelity and degree of completion; since the paper's Bloch solution gives both states the same relaxation rate, equal completion curves in this setup would falsify the claim that heating is intrinsically faster than cooling.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the open-quantum-systems framework, including the GKSL master equation used to derive the detector's complete dynamics."},{"cited_title":"Hodgkinson and J","cited_arxiv_id":null,"evidence_quote":"Provides the analytic response of UDW detectors on BTZ spacetime, including the boundary-condition dependence of transition rates that this work extends."},{"cited_title":"Benatti and R","cited_arxiv_id":null,"evidence_quote":"Gives the two-atom Kossakowski-coefficient decomposition used to write the Lindblad dissipator for the detector."},{"cited_title":"Ba˜ nados, C","cited_arxiv_id":null,"evidence_quote":"Introduces the BTZ black hole geometry that the whole calculation takes as its spacetime."},{"cited_title":"Ba˜ nados, M","cited_arxiv_id":null,"evidence_quote":"Provides the rotating BTZ metric and the mass/angular-momentum parameterization used throughout the paper."},{"cited_title":"Ib´ a˜ nez, , Dieball, C., Lasanta, A.et al.,Heating and cooling are fundamentally asymmetric and evolve along distinct pathways, Nat","cited_arxiv_id":null,"evidence_quote":"Reports the analogous heating/cooling asymmetry in nonequilibrium systems that the paper claims to find in BTZ spacetime."},{"cited_title":"Moroder, O","cited_arxiv_id":null,"evidence_quote":"Defines the quantum Mpemba effect to which the paper likens its heating/cooling asymmetry."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the information-geometry tools (fidelity, quantum speed, degree of completion) used to quantify the asymmetry."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the relative-entropy formulation of thermalization in Schwarzschild spacetime that precedes the paper's quantum Zeroth Law."},{"cited_title":"Patterson and R","cited_arxiv_id":null,"evidence_quote":"Shows Fisher information as a probe of BTZ spacetime, the precedent for using quantum Fisher information in this setting."}],"review_version":1}