{"id":"3a788a09-6bc2-4b80-80e4-b756621e8e12","arxiv_id":"2507.03752","paper_version":6,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A refined dissipation bound s˙ ≥ I_J(-j) is derived for first-passage currents in Markov chains, implying a speed symmetry for optimal currents and extending the effective-affinity framework to discrete time.","lead":"This paper develops a way to rewrite the average entropy produced up to a random stopping time as a Kullback-Leibler divergence, and uses it to prove a tighter version of a known trade-off between speed, accuracy, and dissipation for fluctuating currents in Markov chains. The new bound implies that optimal currents, which fully account for dissipation, must hit positive and negative thresholds at the same average speed.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Time-reversal identity (58) is only proven for finite state spaces, so the refined bound (17) and the Sec. 7.1 infinite-state extension lack support outside finite X.","rationale":"The reader's weakest assumption correctly identifies the finite-state dependence of Eq. (58) as the most delicate point in the proof of the central claim. The martingale argument in Appendix B.1 uses boundedness of the Perron eigenvector to control boundary terms; this is exactly what finite cardinality provides. The central inequality (17) is nonetheless sound within the paper's explicit finite-state setup: the coarse-graining of ⟨S(T)⟩ is a legitimate KL-divergence data-processing step, Wald's equation is justified by the regenerative argument in Appendix C, and the saddle-point replacement of p_T by a delta function in Sec. 4.2 is valid to leading order under the stated LDP. The typographical issues in Eqs. (62) and (64) are real but do not affect the mathematical content once corrected. Thus the main theorem is not falsified, but the paper's Sec. 7.1 extension to infinite cardinality and Langevin systems is unsupported because the proof of (58) explicitly relies on finiteness. This gap does not change the reader's CONDITIONAL verdict, since the finite-state result stands and the needed correction is a careful restriction or proof of the scope. The concrete test on an infinite-state model would settle whether the extension is actually valid or whether the claims must be narrowed.","tokens_in":36337,"tokens_out":34911,"duration_ms":383932,"concrete_test":"Construct a countable-state birth-death process with transition rates growing with the state index so that the tilted-matrix eigenvector φ_{a*}(x) is unbounded. Numerically or analytically compute the forward splitting probability p_− and the time-reversed splitting probability p†_+ for increasing thresholds ℓ_− and ℓ_+, and test whether |ln p†_+|/|ln p_−| → ℓ_+/ℓ_− as required by Eq. (58). If the ratio does not converge to ℓ_+/ℓ_−, then Eq. (58) fails outside finite X and the Sec. 7.1 infinite-state claim must be retracted or proved by a different argument.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central inequality (17) is obtained by combining the coarse-grained entropy bound (65) with the time-reversal relations (58) and (69). Of these, (58) is the load-bearing step: it converts the splitting probability in the time-reversed process into the forward splitting probability. Its proof in Appendix B.1 applies Doob's optional stopping to the martingale M(t)=φ_a(X(t))exp(-aJ(t)-λ_J(a)t) and requires the Perron eigenvector φ_a to be bounded so that the boundary terms in Eq. (135) can be controlled. This boundedness is guaranteed only when the state space X is finite. The paper's own Sec. 7.1 concedes that Eq. (58) was derived under finite cardinality and cautions against infinite-state extensions. In the same paragraph, however, it asserts that Eqs. (2) and (17) apply to infinite-cardinality Markov jump processes and to overdamped Langevin systems. Since (58) is needed to pass from the time-reversed bound (52) to the forward bound (2), and similarly for the refined bound (17), the infinite-state claim is not a logical consequence of the proof given. This is a scope gap rather than an internal inconsistency: the main theorem is valid under the stated finite-X setup of Sec. 2.1, but the paper's broader claims of generality are not established. The other issues noted by the reader—the typo in Eq. (64), the unstated saddle-point step, and the sketched discrete-time TUR—are less serious because they are either presentational or repairable without changing the finite-state result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies first-passage times T = inf{t : J(t) ∉ (−ℓ−, ℓ+)} for fluctuating currents J in stationary Markov chains with finite state space, in both discrete and continuous time. Its central result is the refined asymptotic dissipation bound s˙ ≥ (ℓ+/⟨T⟩)(|ln p−|/ℓ− + I−(1/j))(1 + o(1)), stated as Eq. (17), together with the equivalent fixed-time form s˙ ≥ I_J(−j), Eq. (18). The derivation combines a coarse-graining of the Kullback-Leibler representation of ⟨S(T)⟩, an asymptotic Wald equality, and martingale/large-deviation relations for the tilted process. The paper also derives the speed symmetry (19)/(80) for optimal currents, extends the effective affinity concept to discrete-time Markov chains, and obtains a generalized first-passage symmetry I−(τ) = Ά+(τ) via the time reversal of the dual Doob-transformed process.","tokens_in":36609,"tokens_out":11261,"duration_ms":137009,"significance":"If the results hold, the paper makes a genuine advance in stochastic thermodynamics: Eq. (17) refines the known first-passage trade-off relation by adding the large-deviation term I−(1/j), providing a strictly stronger bound that is verified in the numerical examples. The derivation of the time-reversal identity (58), previously conjectured, is a valuable technical contribution, and the coarse-graining-at-stopping-times method is conceptually clean. The extension of the effective affinity to discrete time is also useful, especially because the standard parabolic bound does not hold there. The finite-state central theorem is internally consistent and is built on published lemmas rather than on fitting to data; the numerical illustrations support the claims for the toy models studied. The main reservations concern the scope of the claimed generality and a few technical steps in the proof of the refined bound, all of which appear repairable.","major_comments":[{"comment":"The statement in §7.1 that Eqs. (2) and (17) 'apply in general' to Markov jump processes on infinite-cardinality state spaces and to overdamped Langevin processes is not supported by the proof as written. Appendix B.1 uses finiteness of X to bound the Perron eigenvector φ_a and to justify Doob's optional stopping theorem, and the time-reversal identity (58) is load-bearing for passing from the time-reversed bound (52) to the forward bound (2), and similarly from (64)/(69) to (17). Since §7.1 itself concedes that (58) was derived under finite cardinality and defers the infinite-state analysis to future work, the claim of general applicability should be either removed or explicitly labeled as a conjecture.","section":"§7.1 and Appendix B.1"},{"comment":"The derivation of (64) relies on the replacement p_T(ℓ+τ|+) ≈ δ(τ − 1/j), which is used to evaluate the Kullback-Leibler term as ℓ+ I†+(1/j). This is a saddle-point/Laplace approximation that is not justified in the text: a large deviation principle gives exponential decay of p_T but does not by itself imply convergence of the integral of p_T against I†+ without additional assumptions on the rate functions (e.g., regularity, uniqueness of the minimizer, and control of subexponential prefactors). Since this step is necessary to obtain the refined bound (17), the authors should supply a justification or state the required assumptions explicitly.","section":"§4.2, Eqs. (64)–(67)"}],"minor_comments":[{"comment":"The second term on the right-hand side of Eq. (62) duplicates the first term, p+ ln(p+/p†+); presumably it should be p− ln(p−/p†−).","section":"§4.1, Eq. (62)"},{"comment":"As printed, Eq. (64) does not reduce to (17) after substitution of (58). The preceding estimates (65)–(67) suggest that the intended intermediate bound is s˙ ≥ [|ln p†+| + ℓ+ I†+(1/j)]/⟨T⟩, with the prefactor ℓ+ attached only to the rate-function term, not to |ln p†+|/ℓ−.","section":"§4.2, Eq. (64)"},{"comment":"The text describing the right-hand panels of Fig. 6 writes the plotted quantity as (ŝFPR − ŝiFPR)/s˙, whereas the figure caption and the definition of ŝiFPR in Eq. (99) indicate the plotted quantity is (ŝiFPR − ŝFPR)/s˙; the sign convention should be made consistent.","section":"§6.1, text near Fig. 6"},{"comment":"The discrete-time thermodynamic uncertainty relation (115) is stated with a brief citation to Ref. [54], but the identity (117) relating the variance of J to the conditional Fano factor of T is only sketched; a few lines of derivation would make the discrete-time extension easier to verify.","section":"§7.2, Eq. (115)"}],"recommendation":"major_revision","confidential_remarks":"The paper's core finite-state result appears sound and the novelty relative to the authors' prior work (Refs. [24,25,31]) is substantial enough for the journal. The main worry is not circularity — the cited martingale and effective-affinity lemmas are published and are not equivalent to the target claim — but the gap between the stated theorem and the claimed infinite-state/Langevin generality, and the unstated saddle-point step in the derivation of (17). Both are fixable within the manuscript's scope. The numerical section is modest but adequate as illustration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Plain take: this is a solid paper with genuinely new results. The refined bound (17), the equivalent fixed-time bound sdot >= I_J(-j), the necessary speed symmetry (19) for optimal currents, and the generalized first-passage symmetry (88) are real advances. The coarse-graining of <S(T)> as a Kullback-Leibler divergence is a nice methodological step, and extending the effective-affinity framework to discrete-time Markov chains is a clean contribution that previous parabolic-bound proofs could not reach. The two toy-model examples support the claims and even exhibit currents in J_v \\ J_sym, which helps map the Venn diagram. The citation pattern is fine: Refs. 24, 25, and 31 are published lemmas, not circular dependencies.\n\nSoft spots, in proportion. The most important is a scope gap: Sec. 7.1 claims that Eqs. (2) and (17) apply to infinite-cardinality Markov chains and overdamped Langevin processes, but the proof of the key time-reversal identity (58) in Appendix B.1 uses boundedness of the Perron eigenvector, which is only guaranteed for finite X. The authors explicitly note that (58) was derived under finite cardinality, yet still make the infinite-state claim in the same paragraph. As written, the infinite-state extension does not follow from the proof. This does not undermine the finite-state theorem, but the overclaim should be trimmed or proven.\n\nSecond, the step in Sec. 4.2 that replaces p_T(ell+ tau | +) with a delta function at tau = 1/j is an unstated saddle-point approximation. It is plausible and standard, but it is load-bearing for the refined bound and should be justified or explicitly stated as an assumption. This is repairable, but as written it is a genuine gap in the derivation.\n\nThird, the discrete-time TUR (115) is stated without proof; the identities (116)-(117) are asserted but not derived. This is a minor issue for the main thread, but a referee should ask for the derivation or a reference. I also did not verify the possible typo in Eq. (64) flagged by the reader; it did not affect my reading of the main argument.\n\nWho should read this: stochastic thermodynamics people working on first-passage problems, thermodynamic inference from dwell times and backstep statistics, and anyone building coarse-grained descriptions of molecular motors. The finite-state results are likely correct and useful. I would send this to a serious referee, and my own verdict is conditional: accept after the infinite-state overclaim is fixed and the saddle-point step is either proven or carefully stated as an assumption.","headline":"Genuinely new refined dissipation bounds and a necessary speed-symmetry condition for optimal currents, with the main finite-state results looking solid; the paper overclaims infinite-state generality in Sec. 7.1 but is well worth refereeing.","tokens_in":37183,"tokens_out":3696,"would_cite":true,"duration_ms":43252,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60J27","60F10","60G40","82C31"],"pacs":["05.70.Ln","05.40.-a","02.50.Ga"],"model":"deepseek-v4-flash","headline":"This paper develops a martingale-based coarse-graining method to bound the entropy-production rate of a stationary Markov chain from the first-passage statistics of a fluctuating current, yielding a refined dissipation inequality and…","keywords":["stochastic thermodynamics","first-passage times","fluctuating currents","entropy production bounds","effective affinity","martingale methods","large deviations","speed-accuracy trade-off"],"falsifier":"Simulate a finite-state nonequilibrium Markov chain with a known non-optimal current, evaluate $\\dot{s}$, $p_-$, $\\langle T\\rangle$, and the rate function $I_-$ at $\\tau=1/j$ for large thresholds, and check the inequality $\\dot{s} \\ge (\\ell_+/\\langle T\\rangle)(|\\ln p_-|/\\ell_- + I_-(1/j))$; a violation at large $\\ell_{\\min}$ would falsify the refined bound. Alternatively, for a current predicted to be optimal, measure the two mean first-passage speeds and check whether they are equal.","tokens_in":36053,"feed_emoji":"⚡","tokens_out":9227,"duration_ms":86794,"temperature":0.7,"pith_summary":"The paper aims to establish a tighter thermodynamic bound for first-passage problems of fluctuating currents: the dissipation rate $\\dot{s}$ is bounded below by $(\\ell_+/\\langle T\\rangle)(|\\ln p_-|/\\ell_- + I_-(1/j))$, where $p_-$ is the splitting probability, $\\langle T\\rangle$ the mean first-passage time, and $I_-$ the large-deviation rate function of the first-passage time at the negative threshold. This refines the known speed-accuracy-dissipation trade-off, which involves only $p_-$ and $\\langle T\\rangle$, by additionally capturing the shape of the first-passage time distribution. A direct consequence is that optimal currents, for which dissipation is fully accounted for by the effective affinity, must satisfy a speed symmetry: the average speed toward the positive threshold equals the average speed toward the negative threshold. The derivation works for both continuous- and discrete-time Markov chains, thereby extending the notion of effective affinity to discrete time. This matters because the relevant quantities are experimentally accessible in systems such as molecular motors, where dwell times and backward-step probabilities can be measured.","feed_headline":"Dissipation bound sharpened by first-passage time statistics","feed_subtitle":"Adds hitting-time statistics to the speed-accuracy trade-off and shows optimal currents obey a speed symmetry.","key_machinery":"The central object is the average entropy production evaluated at the stopping time, $\\langle S(T)\\rangle$, expressed as a Kullback-Leibler divergence between the forward and time-reversed distributions over stopped trajectories $X_0^T$. Coarse-graining this divergence with the observable $D=\\operatorname{sign}(J(T))$ yields the standard bound; coarse-graining with the pair $(D,T)$ yields the refined bound. Martingale theory carries the time-reversal step: the tilted martingale $M(t)=\\phi_a(X(t))e^{-aJ(t)-\\lambda_J(a)t}$, together with Doob's optional stopping theorem, connects first-passage quantities in the time-reversed chain to those in the forward chain, producing the identities $|\\ln p^\\dagger_+|/\\ell_+ = |\\ln p_-|/\\ell_-$ and $I_- = I^\\dagger_+$. The dual process, the Doob transform of the tilted chain at the effective affinity $a^*$, provides the conjugate process in which the generalized symmetry holds.","core_discovery":"The central claim is the refined asymptotic dissipation bound (Eq. 17): for stationary Markov chains on a finite state space, with a fluctuating current $J(t)$ of positive average rate $j$, the entropy production rate satisfies $$\\dot{s} \\ge (\\ell_+/\\langle T\\rangle)\\left(\\frac{|\\ln p_-|}{\\ell_-} + I_-(1/j)\\right)(1+o_{\\ell_{\\min}}(1)),$$ which is equivalent to $\\dot{s}\\ge I_J(-j)$, the large-deviation rate function of the current evaluated against its typical direction. The earlier bound $\\dot{s}\\ge (\\ell_+/\\ell_-)|\\ln p_-|/\\langle T\\rangle$ corresponds to dropping the positive term $I_-(1/j)$. The new term encodes the fluctuations of the first-passage time at the negative threshold, and its inclusion forces optimal currents (those with $\\dot{s}=j a^*$) to satisfy the speed symmetry $\\lim_{\\ell_+\\to\\infty}\\langle T\\rangle_+/\\ell_+ = \\lim_{\\ell_-\\to\\infty}\\langle T\\rangle_-/\\ell_-$. The paper also establishes the generalized first-passage symmetry $I_-(\\tau)=\\hat{I}^\\dagger_+(\\tau)$ for generic currents, with respect to the time-reversal of the dual process defined by the Doob transform at the effective affinity.","pith_inferences":["The speed symmetry is directly testable in single-molecule experiments: if mean dwell times for forward and backward steps of a motor are found equal but the current is not optimal, the motor's positional current lies in the set $J_v\\setminus J_{\\rm opt}$, which would constrain thermodynamically consistent coarse-grained models.","The same coarse-graining-of-Kullback-Leibler-divergence-at-stopping-times scheme could generate a hierarchy of bounds by conditioning on richer functionals of $X_0^T$, such as the full empirical distribution of states, potentially approaching $\\dot{s}$ from below with more detailed observations.","The equivalence $\\dot{s}\\ge I_J(-j)$ suggests a link between the refined first-passage bound and fixed-time thermodynamic uncertainty relations for current fluctuations; one could test whether the bound remains tight for currents that saturate the Gallavotti-Cohen symmetry."],"forward_implications":["The refined inequality $\\dot{s} \\ge (\\ell_+/\\langle T\\rangle)(|\\ln p_-|/\\ell_- + I_-(1/j))$ strictly improves the earlier first-passage trade-off relation whenever $I_-(1/j)>0$, giving a tighter lower bound on dissipation from the same kind of measurements.","Optimal currents must obey the speed symmetry $\\lim_{\\ell_+\\to\\infty}\\langle T\\rangle_+/\\ell_+ = \\lim_{\\ell_-\\to\\infty}\\langle T\\rangle_-/\\ell_-$; this is a necessary condition for optimality, but not sufficient.","The effective affinity $a^*$, the exponential decay constant of the splitting probability, is well defined for discrete-time Markov chains as well, so dissipation bounds and inference schemes based on it apply beyond continuous time.","Every fluctuating current satisfies the generalized symmetry $I_-(\\tau) = \\hat{I}^\\dagger_+(\\tau)$, meaning the negative-threshold first-passage statistics equal the positive-threshold statistics in the time-reversed dual process.","For observables that are not fluctuating currents (e.g., in systems with magnetic fields), the inequalities (112) and (113) still hold, showing that the trade-off is fundamentally between dissipation and accuracy in the time-reversed dynamics."],"supporting_citations":[{"why":"Defines the effective affinity and cycle equivalence classes for generic currents; supplies the splitting-probability decay and the optimality criterion used here.","marker":"[25]"},{"why":"Provides the martingale treatment of first-passage problems for time-additive observables and identifies the dual process whose time-reversal defines the conjugate process.","marker":"[31]"},{"why":"Establishes the large-deviation principle and scaled cumulant generating functions for first-passage times at positive and negative thresholds, used in the refined bound.","marker":"[30]"},{"why":"Derives the earlier speed-accuracy-dissipation bound and conjectures the time-reversal identity for splitting probabilities that this paper proves.","marker":"[24]"},{"why":"Introduces the original first-passage trade-off relation between speed, accuracy, and dissipation.","marker":"[23]"},{"why":"Provides the martingale and optional stopping framework for entropy production at stopping times used throughout the derivations.","marker":"[49]"},{"why":"Supplies the sequential-hypothesis-testing formalism for coarse-graining Kullback-Leibler divergences, the basis of the entropy-production coarse-graining lemma.","marker":"[78]"},{"why":"Wald's equation links the average entropy production at stopping times to the dissipation rate times the mean first-passage time.","marker":"[79]"}],"fun_headline_variants":["First-passage fluctuations tighten dissipation bound","Optimal currents satisfy a universal speed symmetry","Effective affinity works for discrete-time Markov chains","New bound links entropy production to hitting times"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes the state space of the Markov chain is finite, so the eigenvector $\\phi_a$ of the tilted martingale is bounded and optional stopping applies; the key time-reversal identity (58) is proved only under that finite-cardinality assumption, as the authors note in Section 7.1.","fun_headline_variants_meta":{"raw":{"variants":["First-passage fluctuations tighten dissipation bound","Optimal currents satisfy a universal speed symmetry","Effective affinity works for discrete-time Markov chains","New bound links entropy production to hitting times"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000429,"raw_usage":{"total_tokens":2214,"prompt_tokens":984,"completion_tokens":1230,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":1176}},"tokens_in":600,"tokens_out":1230,"duration_ms":10482,"temperature":1.0,"reasoning_tokens":1176,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:06:15.014507+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a finite-state nonequilibrium Markov chain with a known non-optimal current, evaluate $\\dot{s}$, $p_-$, $\\langle T\\rangle$, and the rate function $I_-$ at $\\tau=1/j$ for large thresholds, and check the inequality $\\dot{s} \\ge (\\ell_+/\\langle T\\rangle)(|\\ln p_-|/\\ell_- + I_-(1/j))$; a violation at large $\\ell_{\\min}$ would falsify the refined bound. Alternatively, for a current predicted to be optimal, measure the two mean first-passage speeds and check whether they are equal.","supporting_citations":[{"cited_title":"Effective affinity for generic currents in nonequilib- rium processes,","cited_arxiv_id":null,"evidence_quote":"Defines the effective affinity and cycle equivalence classes for generic currents; supplies the splitting-probability decay and the optimality criterion used here."},{"cited_title":"Martingale approach for first-passage problems of time-additive observables in Markov processes,","cited_arxiv_id":null,"evidence_quote":"Provides the martingale treatment of first-passage problems for time-additive observables and identifies the dual process whose time-reversal defines the conjugate process."},{"cited_title":"Fundamental bounds on first passage time fluctuations for currents,","cited_arxiv_id":null,"evidence_quote":"Establishes the large-deviation principle and scaled cumulant generating functions for first-passage times at positive and negative thresholds, used in the refined bound."},{"cited_title":"Universal tradeoff relation between speed, uncertainty, and dissipa- tion in nonequilibrium stationary states,","cited_arxiv_id":null,"evidence_quote":"Derives the earlier speed-accuracy-dissipation bound and conjectures the time-reversal identity for splitting probabilities that this paper proves."},{"cited_title":"Decision making in the arrow of time,","cited_arxiv_id":null,"evidence_quote":"Introduces the original first-passage trade-off relation between speed, accuracy, and dissipation."},{"cited_title":"Martingales for physicists: A treatise on stochastic thermo- dynamics and beyond,","cited_arxiv_id":null,"evidence_quote":"Provides the martingale and optional stopping framework for entropy production at stopping times used throughout the derivations."},{"cited_title":"Tartakovsky, I","cited_arxiv_id":null,"evidence_quote":"Supplies the sequential-hypothesis-testing formalism for coarse-graining Kullback-Leibler divergences, the basis of the entropy-production coarse-graining lemma."},{"cited_title":"On cumulative sums of random variables,","cited_arxiv_id":null,"evidence_quote":"Wald's equation links the average entropy production at stopping times to the dissipation rate times the mean first-passage time."}],"review_version":1}