{"id":"b7fbbe65-eddc-4348-af04-637a2d36ffd9","arxiv_id":"2507.04669","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A colder initial state reaches a higher-energy prethermal plateau faster than a hotter state in a driven isolated quantum system, a new prethermal inverse Mpemba effect.","lead":"This paper shows that a quantum system can heat up faster when it starts colder, during the intermediate prethermal stage before full thermalization. It demonstrates this in a periodically driven fermion chain and proposes a general mechanism for such prethermal inverse Mpemba effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The prethermal energy for β^-1=0.1 is averaged over a window where the energy is still drifting, so the Eq. (2) criteria may depend on the arbitrary window choice.","rationale":"The reader's conditional verdict already flags the timescale separation and the operational definition of the prethermal energy. My analysis sharpens this to a concrete, testable failure mode: the cold-state energy curve appears to be still decreasing within the chosen averaging window, so the prethermal energy and the resulting t* may be window-dependent. This is the most load-bearing issue because both inequalities in Eq. (2) directly depend on Epre_β. I also note a definitional mismatch: Eq. (2) does not actually require the cold state to reach a higher prethermal energy than the hot state, so the paper's title and abstract ascribe a stronger property than the formal criterion states. The numerical evidence appears to show the stronger property in the plotted data, but the written criterion should be corrected. These concerns do not invalidate the paper's core idea but do justify the conditional verdict pending a systematic window-sensitivity test and a clarified definition.","tokens_in":12049,"tokens_out":12473,"duration_ms":136662,"concrete_test":"For both β^-1=0.1 and 0.5, compute Eβ(t) out to t/T=500; define Epre_β from non-overlapping windows [10,20], [40,50], [100,200], and [300,400]; recompute t*_β and the two inequalities in Eq. (2) for each window. If t*_0.1 ≥ t*_0.5 for any window, or if the gap inequality reverses, the claimed effect is an artifact of the [40,50] window. Also report whether Eβ(t) for β^-1=0.1 is monotonic decreasing at t/T=50; a monotonic drift implies no plateau and no well-defined prethermal energy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Fig. 3(a) states that for β^-1=0.1 the prethermal-state energy appears near t~O(10T) and subsequently decreases toward the infinite-temperature value. Thus the energy at the averaging window t/T∈[40,50] (used to define Epre_β) is not stationary. Because t*_β is defined by |Epre_β − Eβ(t*)| = δ|Epre_β − Eβ(0)|, a later window with lower Epre_0.1 yields a larger gap and a longer t*_0.1, potentially reversing the first criterion in Eq. (2). The paper asserts without systematic test that other windows do not significantly affect the relaxation time, but it does not test the sensitivity of the second criterion or the cold-state t*. Separately, Eq. (2) requires only that the energy gap Epre_β − Eβ(0) is larger for the cold state; it does not require Epre_low > Epre_high, so the stated criterion is weaker than the title's 'heating to a higher prethermal energy.'","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a prethermal inverse Mpemba effect (IME): in an isolated, periodically driven quantum system, a state initialized at a lower temperature can heat up faster and absorb more energy en route to a long-lived prethermal state than a state initialized at a higher temperature. The authors define quantitative criteria in Eq. (2) in terms of a relaxation time t* to a prethermal energy Epre_β, and demonstrate the effect numerically in a one-dimensional spinless fermion chain (chain A) weakly coupled to an ancilla chain (chain B), driven by a periodic gauge field. Using canonical thermal pure quantum states, they show energy trajectories crossing, a rapid saturation of the chain-A normalized inverse participation ratio (NIPR_A ≈ 1), and a two-stage relaxation in which global thermalization occurs on a much longer timescale. A heuristic mechanism is then proposed based on particle-number conservation, weakly coupled sectors, differing energy bandwidths, and asymmetric heating rates of the two chains.","tokens_in":12243,"tokens_out":5531,"duration_ms":62944,"significance":"If the result is robust, it extends the Mpemba/IME phenomenon from relaxation to thermal equilibrium to relaxation toward prethermal states in closed quantum systems, which is a conceptually valuable and potentially experimentally accessible generalization. The numerical strategy—using canonical thermal pure quantum states, NIPR diagnostics, and entanglement-entropy crossing—is well suited to the claim and the two-stage relaxation evidenced in Figs. 2 and 3 is compelling. However, the central demonstration depends on operational definitions (the averaging window for Epre_β and the threshold δ) and on a criterion in Eq. (2) that is weaker than the title's literal claim of heating to a higher prethermal energy. These points need to be tightened before the paper's main assertion is fully supported.","major_comments":[{"comment":"The prethermal energy Epre_β is defined as the average of the energy over t/T ∈ [40,50], but Fig. 3(a) and the accompanying text state that for β^{-1}=0.1 the energy is still drifting downward in this window, decreasing toward the infinite-temperature value. The sentence 'Estimating the prethermal energy over different time intervals does not significantly affect the behavior of the prethermal relaxation time' is not backed by a systematic test. Since the inequalities in Eq. (2) and the extracted t*_β values both depend on Epre_β, the demonstrated IME could in principle be an artifact of the chosen window. Please provide a sensitivity analysis over several averaging windows (e.g., [30,40], [50,60], [70,80]) and over several values of δ, showing that the ordering t*(β=0.1) < t*(β=0.5) and the second criterion in Eq. (2) are stable.","section":"Demonstration with a simple model, Fig. 3(a)"},{"comment":"The second line of Eq. (2) requires Epre_βℓ − Eβℓ(0) > Epre_βh − Eβh(0), which is a statement about energy uptake, not about the ordering of the prethermal energies themselves. Because Eβℓ(0) < Eβh(0), this inequality can hold even when Epre_βℓ < Epre_βh, i.e., even when the colder state does not heat to a higher prethermal energy. The abstract and title claim that the colder state 'heats up ... to a higher prethermal energy,' so the criterion in Eq. (2) is weaker than the stated phenomenon. Please either add the condition Epre_βℓ > Epre_βh or revise the terminology to describe a larger energy-gap condition rather than a higher prethermal energy.","section":"Eq. (2) and abstract/title"},{"comment":"The proposed general mechanism (Sec. 'Mechanism and generalization') is presented as universal and controllable, but the timescale separation between fast intra-chain heating and slow inter-chain particle transfer is only observed for one parameter set (JA=VA=1, J⊥=0.04, Ω=1, A0=1) and is not derived from a controlled approximation. The paper would be substantially strengthened by a parameter sweep showing that the prethermal IME disappears as J⊥/JA grows or as the drive frequency changes in the directions predicted by the mechanism, thereby testing the claimed universality.","section":"Mechanism and generalization"}],"minor_comments":[{"comment":"The inset shows relaxation times t*/T as a function of β^{-1} without markers or error bars; please clarify whether these are single estimates or averaged over the ten samples, and include the bootstrap standard errors shown elsewhere.","section":"Fig. 2(b) inset"},{"comment":"The caption of Fig. 3 contains a duplicated '(b)(b)' typographical error in the second panel label.","section":"Fig. 3 caption"},{"comment":"The ensemble average over random vectors is indicated by an overline in Eq. (4), but the notation is not defined in the equation itself; please define it in the text immediately preceding the equation.","section":"Eq. (4)"},{"comment":"When stating that the high-temperature random state gives energy VA/2 * N(N−1)/(L(L−1)), the text should specify that this is the per-site interaction energy and that the kinetic energy averages to zero under the random-state assumption.","section":"High-temperature energy estimate"},{"comment":"The caption refers to panels (a) and (b), but the figure panels are not labeled in the displayed schematic; please add the labels.","section":"Fig. 4 caption"},{"comment":"The temperature dependence of NIPR_B is described as nonmonotonic, but the physical interpretation would be clearer if the text explained why NIPR_B returns to ≈1 at low temperatures (vacuum state) and how this relates to the prethermal IME mechanism.","section":"End Matter, Fig. 6"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely within scope for a rapid-communication journal and the numerical observation is interesting, but the window-sensitivity issue is load-bearing for the main claim. I recommend major revision rather than rejection because the requested checks are feasible within the manuscript's scope. The authors should also be asked to reconcile the title/abstract wording with the actual inequality in Eq. (2)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this paper identifies a genuinely new effect—an inverse Mpemba effect in the approach to a prethermal state—and gives a clean numerical demonstration in a small driven fermion chain. I think the idea is real and worth referee time, but the demonstration has one operational soft spot that the authors should be asked to fix before publication.\n\nWhat's new: the definition in Eq. (2) is a sensible extension of the IME condition from a true thermal state to a prethermal one, and I cannot find it in the cited literature. The numerical evidence is internally consistent: the energy curves cross, NIPR_A saturates near 1 for the cold state, and the long-time data in Fig. 3 show the expected two-stage relaxation to infinite temperature. The End Matter temperature-dependent particle distributions support the proposed mechanism, and the mechanism itself—weakly coupled sectors plus a fast-heating subsystem whose spectrum contains the slow one—is a plausible and testable picture. Citations are appropriate and the numerical methods are standard.\n\nThe soft spots are proportionately real. First, the prethermal energy is defined by averaging over t/T ∈ [40,50], but for β^{-1}=0.1 the energy is still drifting in that window: Fig. 3(a) shows the energy peaking near t~10T and then decreasing toward the infinite-temperature value. That means t*_β is defined against a moving reference, and the stress-test concern that a later window could lengthen t* for the cold state is not addressed. The paper's one-sentence claim that other intervals don't change the behavior needs a real test, not an assertion. Second, the whole demonstration is a single parameter set (J⊥=0.04, 36 sites, 6 fermions). No finite-size scaling, no scan over driving parameters, so the broader controllability claim outruns the evidence. Third, the criterion in Eq. (2) is weaker than the title's 'heating to a higher prethermal energy': it only requires a larger energy gap for the cold state, not Epre_cold > Epre_hot. The plotted data happen to show the cold state higher, but the formal definition should match the claim. These are fixable issues.\n\nWho this is for: anyone working on quantum Mpemba effects, Floquet prethermalization, or the thermodynamics of driven quantum systems. It deserves a serious referee; I would send it back with a request for the window-insensitivity test and broader parameter scans. If those check out, the result stands.","headline":"Genuinely new prethermal IME with a clean but narrow numerical demonstration; the window-dependence of the prethermal energy needs testing before I'd trust the headline claim.","tokens_in":12780,"tokens_out":3403,"would_cite":true,"duration_ms":36119,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper demonstrates that a colder initial state can heat up faster and reach a higher-energy plateau than a warmer initial state during prethermalization in a periodically driven fermion chain.","keywords":["prethermalization","inverse Mpemba effect","periodically driven quantum systems","Floquet dynamics","thermal pure quantum states","weakly coupled subsystems","quantum thermalization","entanglement entropy"],"falsifier":"Repeat the simulation with larger system sizes or smaller $J_\\perp$ and check whether the $\\beta^{-1}=0.1$ trajectory still crosses the $\\beta^{-1}=0.5$ trajectory and whether the prethermal energy (the average over $t/T\\in[40,50]$) remains stable when the averaging window is shifted to $[60,70]$ or $[80,90]$; if the crossing disappears or the plateau drifts toward infinite-temperature energy on the same timescale as the crossing, the prethermal IME claim would be falsified.","tokens_in":11829,"feed_emoji":"♨️","tokens_out":5666,"duration_ms":57413,"temperature":0.7,"pith_summary":"The paper introduces the prethermal inverse Mpemba effect: during relaxation toward a long-lived prethermal state, a system initialized at lower temperature can heat up faster and to a higher energy than one initialized at higher temperature. It proves the concept by simulating a one-dimensional spinless fermion chain weakly coupled to an ancilla chain and driven by a periodic gauge field on one leg. The cold initial state ($\\beta^{-1}=0.1$) reaches its prethermal plateau sooner and at higher energy than the warm state ($\\beta^{-1}=0.5$), satisfying both criteria of their Eq. (2). The authors also sketch a general mechanism---conserved particle number dividing Hilbert space into weakly coupled sectors, with one subsystem heating rapidly and the other slowly---so the effect should transfer to other driven platforms. If correct, the Mpemba phenomenon is not limited to final thermal equilibrium but appears throughout multistage relaxation, with implications for energy control in driven quantum systems.","feed_headline":"A colder fermion chain out-heats a warmer one before thermalizing","feed_subtitle":"Periodic driving on one leg of a two-leg fermion ladder makes the cold initial state reach a higher prethermal plateau sooner.","key_machinery":"The core object is the two-leg fermion lattice with Hamiltonian $\\hat{H}_0 = -J_A\\sum_j(\\hat{c}^\\dagger_{j,A}\\hat{c}_{j+1,A}+\\mathrm{h.c.}) + V_A\\sum_j \\hat{n}_{j,A}\\hat{n}_{j+1,A} - J_\\perp\\sum_j(\\hat{c}^\\dagger_{j,A}\\hat{c}_{j,B}+\\mathrm{h.c.})$, driven through a Peierls phase on chain A only. The central mechanism is the combination of weak interchain coupling $J_\\perp$ and particle-number conservation, which partitions the Hilbert space into sectors $(N_A,N_B)$ that communicate only on long timescales. The Floquet drive heats chain A quickly while chain B remains cold; the observable $\\mathrm{NIPR}_A$, built from the Schmidt decomposition and normalized so that a completely random state gives $1$, diagnoses when chain A has prethermalized. The energy-spectrum inclusion $[E_B^{\\min},E_B^{\\max}]\\subset[E_A^{\\min},E_A^{\\max}]$ ensures the cold initial state, with particles concentrated in A, can absorb energy to the top of A's band, producing both a faster and a higher prethermal plateau.","core_discovery":"The central claim is that the inverse Mpemba effect occurs not only for relaxation to true thermal equilibrium, but also for relaxation to a prethermal state in an isolated, periodically driven quantum system. In the model studied---a chain of interacting spinless fermions (chain A) coupled by weak hopping $J_\\perp=0.04$ to an undriven ancilla chain (chain B), with total particle number conserved---the state prepared at inverse temperature $\\beta^{-1}=0.1$ has a shorter prethermal relaxation time and a larger energy gap between its initial and prethermal energies than the state at $\\beta^{-1}=0.5$. The crossing of the energy trajectories and the crossing of the subsystem inverse-participation-ratio curves $\\mathrm{NIPR}_A$ indicate that chain A has fully randomized while global thermalization is still suppressed, giving a two-stage relaxation. The authors argue the mechanism is generic: a conserved quantity splits the Hilbert space into weakly coupled sectors, the fast-heating subsystem has a broader energy spectrum that contains the slow subsystem's spectrum, and at low initial temperatures more particles sit in the fast-heating subsystem.","pith_inferences":["A natural extension the authors leave implicit: the speedup may be tunable by shaping the drive spectrum, for instance by driving chain A harder or chain B at a higher frequency, rather than by changing only the initial temperature.","One testable prediction is that the effect should vanish or reverse when $J_\\perp$ becomes comparable to $J_A$, since the sector bottleneck disappears and the two chains thermalize together.","The criterion in Eq. (2) could be recast in terms of thermomajorization or phase-space distances, potentially linking prethermal IME to non-monotonic relaxation rates in Markovian settings.","A possible concern: the observed crossing may depend on the finite particle density $N/L$; checking whether the effect survives at higher densities would clarify whether it is a generic feature or specific to dilute fillings."],"forward_implications":["If the mechanism is generic, prethermal IME should appear in any driven system with a conserved quantity and weakly coupled subsystems whose spectra overlap unevenly.","Cold-atom ladders, superconducting qubit arrays with conserved particle number or parity, and Rydberg chains are concrete platforms where the crossing could be searched for.","The effect turns the Mpemba phenomenon into a multistage phenomenon, so relaxation protocols in quantum control may be able to exploit faster and higher energy uptake before full thermalization.","Because the entanglement entropy also shows a crossing, the prethermal IME has a quantum-information signature, not just an energy signature."],"supporting_citations":[{"why":"Defines the inverse Mpemba effect criterion (energies ordered by initial temperature and faster relaxation from the colder state) that the paper extends to prethermal states.","marker":"[4]"},{"why":"Supplies the Floquet-Magnus theory showing slow energy absorption in high-frequency driven systems, underpinning the prethermal regime.","marker":"[43]"},{"why":"Provides a rigorous bound on energy absorption in periodically driven quantum systems, supporting the existence of the prethermal plateau.","marker":"[44]"},{"why":"Establishes long-time Floquet thermalization to infinite temperature in isolated driven interacting systems, the eventual fate in the model.","marker":"[41]"},{"why":"Supplies the canonical thermal pure quantum state method used to prepare finite-temperature initial states for the numerics.","marker":"[49]"},{"why":"Introduces the canonical thermal pure quantum state formalism used for the initial states.","marker":"[50]"},{"why":"Gives the NIPR value $2/(D+1)$ for a completely random state, the reference used to define $\\mathrm{NIPR}_A$.","marker":"[55]"},{"why":"Provides the time-dependent Lanczos algorithm used for the real- and imaginary-time evolution in the numerical simulations.","marker":"[59]"}],"fun_headline_variants":["Cold fermion ladder prethermalizes faster than a warm one","Prethermal inverse Mpemba: colder state relaxes quicker under driving","Cold initial state beats warm in race to prethermal plateau","Driven fermions show inverse Mpemba effect in prethermal state","Colder start reaches prethermal state before warmer one"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The demonstration rests on an assumed timescale separation: with $J_\\perp=0.04$ the weak interchain hopping keeps the two chains nearly decoupled long enough for chain A to prethermalize within the observation window, and this separation is read off the numerics rather than derived from a controlled approximation.","fun_headline_variants_meta":{"raw":{"variants":["Cold fermion ladder prethermalizes faster than a warm one","Prethermal inverse Mpemba: colder state relaxes quicker under driving","Cold initial state beats warm in race to prethermal plateau","Driven fermions show inverse Mpemba effect in prethermal state","Colder start reaches prethermal state before warmer one"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001034,"raw_usage":{"total_tokens":4308,"prompt_tokens":854,"completion_tokens":3454,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":470,"completion_tokens_details":{"reasoning_tokens":3367}},"tokens_in":470,"tokens_out":3454,"duration_ms":27423,"temperature":1.0,"reasoning_tokens":3367,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:42:37.568878+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the simulation with larger system sizes or smaller $J_\\perp$ and check whether the $\\beta^{-1}=0.1$ trajectory still crosses the $\\beta^{-1}=0.5$ trajectory and whether the prethermal energy (the average over $t/T\\in[40,50]$) remains stable when the averaging window is shifted to $[60,70]$ or $[80,90]$; if the crossing disappears or the plateau drifts toward infinite-temperature energy on the same timescale as the crossing, the prethermal IME claim would be falsified.","supporting_citations":[{"cited_title":"Kuwahara, T","cited_arxiv_id":null,"evidence_quote":"Supplies the Floquet-Magnus theory showing slow energy absorption in high-frequency driven systems, underpinning the prethermal regime."},{"cited_title":"Sugiura and A","cited_arxiv_id":null,"evidence_quote":"Introduces the canonical thermal pure quantum state formalism used for the initial states."},{"cited_title":"Kaplan, F","cited_arxiv_id":null,"evidence_quote":"Gives the NIPR value $2/(D+1)$ for a completely random state, the reference used to define $\\mathrm{NIPR}_A$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the time-dependent Lanczos algorithm used for the real- and imaginary-time evolution in the numerical simulations."}],"review_version":1}