{"id":"198f268a-1ff9-4043-87b9-6a32ec2054cd","arxiv_id":"2412.07706","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"For a particle hopping between passive and active baths, heat-exchange fluctuation theorems remain linear, and the implied active-bath temperature equals the kinetic temperature for jump-carried heat but is higher for work-based heat.","lead":"A numerical study measures how an active (out-of-equilibrium) bath exchanges heat with a passive bath through a particle jumping in a double-well potential. It finds that a fluctuation theorem still holds, and the temperature it implies depends on how heat is defined, matching the kinetic temperature for one definition.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The active-bath claim hinges on finite-time fits of Eq. (21); for the work-like heat q_W the rate-function convergence is not established, so T_FT^W may be a fit parameter rather than a true thermodynamic temperature.","rationale":"The reader's weakest assumption is exactly the convergence of the finite-time curves to the large-deviation rate functions, checked only by visual overlap for q_E and even less convincingly for q_W. My independent reading of the figures supports this: Fig. 7(a) still shows visible separation between tau = 2e4 and tau = 3e4 curves, while Fig. 7(c) shows a persistent shift between p(q_W) and p(q_E) that the authors attribute to physics but could also indicate incomplete relaxation of the q_W observable. The central claim that a fluctuation theorem with a thermodynamic temperature holds for the active bath rests entirely on these fits, since no analytical derivation is given (the authors themselves call for further validation in the Conclusions). The paper is otherwise internally consistent: the passive-bath case is checked against the known result from Refs. [55,59,60], the heat definitions are clear, and the phenomenology-based interpretation of the q_E result is plausible. But the quantitative temperature values, especially T_FT^W, are not robustly established because the finite-time correction in Eq. (21) is not quantified. The proposed test is a straightforward extension of the existing numerics that would settle whether the residual finite-time effect is negligible. Since the reader already returned a conditional verdict, my read does not change that verdict; the concern sharpens the specific condition that needs to be verified.","tokens_in":23975,"tokens_out":4709,"duration_ms":34875,"concrete_test":"Compute -ln(p(q_W))/tau at tau = 3e4 and 6e4 for Pe=50, with the same number of samples per run, and check whether the curves overlap over the full q range used in the fit (or at least over the linear region of the ratio). Additionally, repeat the fit of Eq. (21) on data subsampled to half the trajectories and on trajectories restarted from the left well, and compare the two fitted T_FT^W values: if they differ by more than the stated fit precision or if the rate-function curves do not overlap, the claim of a converged LDP-based temperature is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central active-bath claim is that Eq. (21) holds for both heat definitions, with T_FT^E matching T_kin and T_FT^W lying between T_kin and T_eff. This requires that the finite-time curves -ln(p(q))/tau have converged to the rate functions I(q), so that the fitted slope is truly I(-q)-I(q). For q_E (Fig. 6b inset) the overlap at tau > 1e4 is presented, though only visually and without error bars. For q_W (Fig. 7a inset) the claim of convergence is even weaker: panel (a) shows curves still separating at large tau, and the inset does not clearly establish overlap. The q_W distribution is also still shifted relative to q_E at tau = 3e4 (Fig. 7c), which the authors reinterpret as a physical effect rather than as evidence of non-convergence. Since the fit for T_FT^W is performed at tau = 3e4 with Tr = T1 fixed a priori, and since no uncertainty analysis or code is provided, the value T_FT^W ~ 0.42 could be a finite-time artifact. The paper itself acknowledges no derivation of the active-case FT, so the numerical fit is the only support. If the rate function has not converged in the sampled q range, the extracted temperature is not a thermodynamic quantity.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper numerically studies heat exchange between two baths that are spatially separated by a double-well potential, with a Brownian particle hopping between the wells. Two heat definitions are used: the kinetic energy carried during jumps (q_E) and the work performed by the particle on the passive bath (q_W). The authors test the fluctuation theorem (Eq. 21), which relates the large-deviation slope to the inverse temperatures of the two baths. In the passive-passive case both heat definitions are reported to satisfy the theorem with the fitted temperatures matching the bath temperatures. In the active case, where the left bath contains an additional Ornstein-Uhlenbeck active noise, the theorem is reported to hold for both heat definitions; the extracted temperature T_FT equals the kinetic temperature for q_E and lies between the kinetic and effective temperatures for q_W. The results are interpreted through the jump phenomenology of the particle, in particular the run-up effect of the active force before a jump.","tokens_in":24312,"tokens_out":5796,"duration_ms":53002,"significance":"If the results are robust, the paper makes a useful contribution to the debate on out-of-equilibrium temperatures for active baths: it provides a concrete setup in which a fluctuation-theorem-based temperature is measurable and differs according to the observable, showing that different heat observables probe different time scales of energy exchange. The manuscript is clearly written and the numerical protocol is well specified, including the parameter choices, the restart protocol for noises, and the comparison with analytical harmonic-limit expressions for kinetic and effective temperatures. The comparison of T_FT with independently defined kinetic and effective temperatures is a genuine external benchmark. The main weakness is that the active-bath claim rests entirely on finite-time convergence of fitted large-deviation curves, and the manuscript does not provide quantitative convergence diagnostics or uncertainties for the extracted temperatures, which is load-bearing for its central message.","major_comments":[{"comment":"The central active-bath claim for q_W rests on the assertion that -ln(p(q_R^W))/tau has converged to the rate function I(q) at the largest sampling times. The evidence in Fig. 7(a) and its inset is not sufficient: the main panel shows curves that are still separating as tau grows, and the inset is described only as showing overlap without a quantitative threshold. Fig. 7(c) shows p(q_R^W) shifted relative to p(q_R^E) at tau = 3e4; the authors interpret this as a physical effect, but a finite-time contribution to the rate function would produce the same observation. Since T_FT^{q_R^W} about 0.42 is obtained by fitting Eq. (21) at tau = 3e4 with T_r = T_1 fixed, this value could be a fit parameter rather than a thermodynamic temperature. Please provide quantitative convergence diagnostics (e.g., collapse of the curves at successive tau, local estimates of I(q) and I(-q)-I(q) with error bars), report the fitted q-range, and propagate the resulting uncertainty to T_FT.","section":"§3.2, Figs. 7(a)-7(c)"},{"comment":"The quantitative claims that T_FT^{q_R^E} coincides with T_kin^dw and that T_FT^{q_R^W} lies strictly between the kinetic and effective temperatures are made without any reported uncertainties. Table 1 lists point values only, and the text describes agreement at the level of two significant digits. For a numerical paper whose main result is a set of temperature comparisons, bootstrap or trajectory-to-trajectory standard errors on T_FT, T_kin, and T_eff are needed; without them the 'exact coincidence' claim is not assessable.","section":"§3.2, Table 1"},{"comment":"The extraction of T_FT assumes that the finite-time ratio (1/tau) ln[p(q)/p(-q)] has reached the asymptotic form I(-q)-I(q). For q_E the inset of Fig. 6(b) gives only visual evidence of overlap at tau > 1e4, with no estimate of the sub-exponential contribution (c(q)-c(-q))/tau. Since the paper offers no analytical derivation of the active-case FT, the numerical convergence is the only support for the claim. Please add a quantitative convergence test for q_E as well, and state the uncertainty of the fit slope for each entry in Table 1.","section":"§2.3, Eq. (21)"}],"minor_comments":[{"comment":"In the definition of Delta U(x(tau)) the text writes U(x(tau)) - U(x(tau)); this should be U(x(tau)) - U(x(0)).","section":"§2.2, Eq. (14)"},{"comment":"The word 'tempexrature' appears in the description of the right-well bath; it should be 'temperature'.","section":"§2.1"},{"comment":"The word 'superscrpits' should be 'superscripts'.","section":"§2.3"},{"comment":"The phrase 'come to depend depend' contains a duplicated word; it should read 'come to depend on'.","section":"§2.2, Eq. (20)"},{"comment":"The parenthetical remark that p(q_R^W) is 'just symmetrical' is inconsistent with Fig. 7(c), which shows an asymmetric p(q_R^W); please correct the remark.","section":"§3.2, parenthetical after Fig. 6(a)"},{"comment":"The expression '-ln(q_R^W)/tau' appears to be missing the distribution symbol; it should read '-ln(p(q_R^W))/tau'.","section":"Fig. 7(a) and accompanying text"},{"comment":"Reference [57] has a malformed URL ('https://bookstore.ams.orgsza/view?...'); please update it.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a numerical study without a code or data availability statement; for a result whose only validation is numerical, adding such a statement would substantially improve verifiability. The extremely large effective temperatures (e.g., T_eff ~ 21 at Pe = 50) compared with T_FT ~ 0.4 make the statement that T_FT^W lies 'between' kinetic and effective temperatures almost trivially true; the authors should clarify whether the comparison with T_eff is intended to be quantitative or merely qualitative."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Let me skip the throat-clearing: this is a solid, mostly numerical paper that does something genuinely useful. It takes the Bodineau-Derrida heat fluctuation theorem, which was established for baths acting simultaneously on a particle, and tests it in a setup where the baths are spatially separated by a double-well barrier and one bath is active (AOUP noise). The new jump-based heat definition Q_E is simple but sensible, and the passive-passive control case checks out: both Q_E and Q_W reproduce the bath temperatures, which gives confidence in the protocol. The active-bath result—FT still appears to hold, with the extracted temperature matching T_kin for Q_E and sitting between T_kin and T_eff for Q_W—is the kind of clean numerical observation that people working on effective temperatures in active matter will want to know about. The interpretation via jump phenomenology (instantaneous kinetic transfer vs. delayed dissipation of excess kinetic energy) is plausible and consistent with the distributions they show.\n\nThe main weaknesses are about how much weight to put on the fitted temperatures, not about the existence of the effect. The FT is checked by fitting Eq. (21), so the theorem's validity is not independently predicted; that is fine for a numerical study, but it means the slope at finite tau is the only support. For Q_E the overlap of -ln(p)/tau curves at large tau is reasonably convincing. For Q_W the convergence claim is weaker: the curves are still shifting at tau ~ 3e4 and the distribution remains offset from p(q_E), which the authors attribute to a physical run-up effect. That may well be right, but with no error bars on the linear fits, no code or data release, and T_r fixed a priori, T_FT^W ~ 0.42 should be treated as a finite-time estimate rather than a sharply resolved thermodynamic temperature. The same caveat applies to the Pe dependence in Table 1. I don't see a load-bearing flaw: the central comparison is externally benchmarked against T_kin and T_eff computed independently, and the passive case validates the method. But the quantitative claims need a reimplementation or uncertainty analysis before they can be used as benchmarks. The citation pattern looks appropriate, with the relevant FT and AOUP literature present.\n\nWho is this for: people working on active-matter effective temperatures and stochastic thermodynamics; it would also work well in a reading group on fluctuation theorems. It deserves a serious referee. I would send it to review and ask for error bars/convergence analysis and, ideally, code/data deposit. If those come back clean, the paper will be a useful reference.","headline":"A clean numerical demonstration that heat-fluctuation-theorem temperatures for an active bath are definition-dependent; the qualitative result holds up, but the quantitative values need uncertainty and convergence analysis before they should be trusted as benchmarks.","tokens_in":24824,"tokens_out":3719,"would_cite":true,"duration_ms":34366,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["05.40.-a","05.70.Ln"],"model":"deepseek-v4-flash","headline":"A heat-exchange fluctuation theorem whose slope is set by inverse-temperature differences still holds when one bath is active, but the recovered temperature depends on how heat is defined.","keywords":["fluctuation theorem","heat exchange","active Ornstein-Uhlenbeck particle","double-well potential","kinetic temperature","effective temperature","large deviation principle","out-of-equilibrium temperature"],"falsifier":"Compute the fitted slope of Eq. (21) at sampling times extending well beyond $\\tau=3\\times10^4$ for $\\mathrm{Pe}=50$, or obtain the rate functions by an independent large-deviation estimator; if the slope changes with $\\tau$ once the sub-exponential shift is removed, then $T_{FT}$ is a finite-time fit parameter rather than a thermodynamic temperature.","tokens_in":23764,"feed_emoji":"🌡️","tokens_out":11587,"duration_ms":95452,"temperature":0.7,"pith_summary":"This paper asks whether the standard heat-exchange fluctuation theorem, $I(-q)-I(q)=(1/T_1-1/T_2)q$, which relates the slope of the large-deviation rate function to the bath temperatures, survives when one of the two baths is an active, out-of-equilibrium bath. The setup is a single particle in a double-well potential, with a passive bath in one well and either another passive bath or an active bath (a passive bath plus an Ornstein-Uhlenbeck coloured noise) in the other; the heat per unit time $q$ is measured two ways: as the kinetic energy the particle carries when it jumps between wells, and as the work it does on the passive bath. The paper finds the theorem holds in every case, for both definitions. In the active case the temperature extracted from the fluctuation-theorem slope is definition-dependent: for jump-energy heat it matches the kinetic temperature of the active bath, while for work heat it is larger, lying between the kinetic and effective temperatures. If correct, this provides a workable way to assign a temperature to an active bath and shows that out of equilibrium the temperature registered by a fluctuation theorem depends on the observable used to define heat.","feed_headline":"Heat fluctuation theorem holds even for an active bath","feed_subtitle":"But the temperature it reports depends on how heat is defined: kinetic for jump energy, higher for work.","key_machinery":"The argument is carried by the large-deviation rate function $I(q)$ for the heat per unit time, through the identity $I(-q)-I(q)=(1/T_r-1/T_l)q$, evaluated operationally as the slope of $\\ln[p(q)/p(-q)]/\\tau$ after the sub-exponential contributions decay. The second element is the double-well geometry that spatially separates the two baths, with the particle mediating heat through jumps. The third is the choice of two heat observables: $q_E$, the sum of kinetic energies carried by the particle at each well crossing, and $q_W$, the Stratonovich work done by the particle against the passive bath. For the active case, the fourth element is the Ornstein-Uhlenbeck coloured noise added to the white-noise bath in the left well (an Active Ornstein-Uhlenbeck particle), with Péclet number controlling activity. Together these pieces turn a fluctuation theorem into a thermometer whose reading depends on the time scale of energy release captured by the chosen heat definition.","core_discovery":"The paper's central claim is that the finite-time form of the heat fluctuation theorem, $\\ln[p(q)/p(-q)]/\\tau \\simeq (1/T_r-1/T_l)q$, holds for heat exchanged between two spatially separated baths even when one bath is active, and that the fitted temperature $T_{FT}$ is physically meaningful but depends on the heat observable. For two equilibrium baths, both heat definitions give slopes equal to the true bath temperatures, and at long times the two rate functions $I(q_E)$ and $I(q_W)$ coincide. With the active bath (an Ornstein-Uhlenbeck noise added in the left well, with $T_1=T_2=0.2$), the theorem still holds, but at Péclet number 50 the temperature extracted from the jump-kinetic-energy heat is $T_{FT}^{q_E}\\simeq 0.3$, equal to the kinetic temperature of the active bath, while the temperature extracted from the work heat is $T_{FT}^{q_W}\\simeq 0.42$, between the kinetic and effective temperatures. The explanation offered is the active noise's run-up effect: the particle is pushed toward the barrier, arrives at the right well with extra velocity, and dissipates the excess not instantaneously at the crossing but during its descent, so instantaneous jump heat registers the kinetic temperature while work heat includes the delayed dissipation.","pith_inferences":["An implication the paper leaves implicit: the gap between $T_{FT}^{q_E}$ and $T_{FT}^{q_W}$ is a ready-made experimental probe of active memory; it should grow with the persistence time $\\tau_p$ and collapse to zero as $\\tau_p\\to 0$, where the active bath becomes passive.","A testable extension would apply the same slope analysis to the joint heat that includes the active work, $q_L^W - w_a$; whether Eq. (21) remains linear there would decide if the fluctuation-theorem temperature is a property of the passive component alone or of the whole active bath.","If the linear-slope behavior persists for $q_E$ at higher Péclet numbers and in other potentials, fluctuation-theorem thermometry could be used in experiments on Janus-particle suspensions or optically trapped tracers to read the kinetic temperature of an active environment through heat statistics alone.","Read as a statement about temperature, the results suggest that an active bath does not have a unique fluctuation-theorem temperature; the temperature is a function of the observable and the timescale over which energy is exchanged."],"forward_implications":["The fluctuation theorem works for spatially separated equilibrium baths, extending the earlier simultaneous-bath results to the double-well geometry.","For the active bath, the fluctuation-theorem temperature extracted from jump-energy heat $q_E$ equals the kinetic temperature, so this heat definition gives an instantaneous, velocity-based temperature.","For work heat $q_W$, the fluctuation-theorem temperature is systematically larger than the kinetic temperature and smaller than the effective one, so different heat observables probe different relaxation timescales of the active bath.","At all Péclet numbers studied, the ordering $T_{kin}^{dw}\\simeq T_{FT}^{q_E}