{"id":"e6a1ce1b-182a-4a99-a2a2-a5e11986dadf","arxiv_id":"1908.07405","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In the large volume limit, switching between states of a multistable non-equilibrium system is governed by entropy produced along the switching path, not by steady-state entropy or entropy production.","lead":"Using fluctuation theorems and Freidlin-Wentzell large deviation theory, the authors derive an approximate maximum entropy production principle for switching paths in multistable non-equilibrium systems, and test it on the Schlögl and toggle switch models. A smart generalist might read this because it offers a thermodynamic criterion for which stable states win in bistable biological, ecological, or climate systems.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The universal MaxEPP claim rests on CA→B≈CB→A; the paper's own data show ~10% failures, so relative stability is not generally controlled by path entropy production alone.","rationale":"The reader's weakest-assumption analysis correctly identifies CA→B ≈ CB→A as the load-bearing step. Equation 19 is an algebraic identity once the action is split into conservative and dissipative parts, so by itself it cannot produce the 'more dissipative switches are more probable' conclusion. That conclusion requires comparing opposing switching paths, which is exactly what Eq. 20 does under the conservative-action equality. The paper's own reported 10% failure rate and its identified failure mode (low-copy-number saddle points) show the approximation is not universal. Because the failure is tied to the local structure of the deterministic force, it is not removed in the large-volume limit unless the saddle concentration also scales with Ω, which the text does not establish. Therefore the central claim should be presented as conditional on this approximation, not as a general thermodynamic principle for multistable systems. I agree with the reader's verdict of CONDITIONAL; my read does not change that verdict. The paper's numerical evidence and explicit statement of the approximation's limits are genuine supporting elements, and the concern is a qualification rather than a refutation.","tokens_in":10349,"tokens_out":5359,"duration_ms":52529,"concrete_test":"For the 100 toggle switch parameter sets (plus additional sets with low-copy-number saddles), compute CA→B and CB→A directly from Eq. 18 along the geometrically minimized paths. Split the sets into those with |CA→B − CB→A|/(CA→B + CB→A) below and above a small threshold (e.g. 5%). Check whether Eq. 20's predicted relation between action differences and path entropy production differences, and the resulting occupation-probability predictions against Gillespie simulations, hold in the first subset but fail systematically in the second. If the failure is confined to the second subset, the universal claim must be restricted; if it appears in both, the issue is more severe than the stated approximation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation 20 is the step that converts the algebraic identity Eq. 19 into the predictive statement that more dissipative switches are exponentially more probable. Its derivation assumes CA→B ≈ CB→A, i.e. that the conservative actions of the two opposing minimum-action paths are nearly equal (Section III, paragraph after Eq. 19). The paper states that this holds for only 90% of the toggle switch parameterizations and that divergence is generally observed when the saddle point sits at low copy number relative to the steady states. This failure is not obviously a finite-volume artifact: the conservative action difference is a property of the deterministic force and diffusion landscape, which persists as Ω grows. Thus, for the excluded parameter sets, the difference in actions is not equal to half the difference in path entropy productions, and the relative stability criterion based on path entropy production alone breaks down. Since the abstract and the Discussion present the MaxEPP for switching paths as a general conclusion about multistable non-equilibrium systems, the unqualified claim overreaches. The paper itself flags the limitation, but the headline conclusion should be explicitly conditional on the conservative-action approximation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper asks which thermodynamic quantities control the relative stability and the switching rates between macrostates of multistable non-equilibrium chemical systems in the large-volume limit. The authors combine the Freidlin–Wentzell (FW) action of the chemical Langevin equation (Eq. 7) with the coarse-grained (Langevin) entropy production along a path, defined via the action difference between forward and time-reversed paths (Eq. 8). Splitting the action into a conservative part C (Eq. 18) and the path entropy production ΔS_L yields Eq. (19), P_A→B = exp(ΔS_L/2 − C)/Q_A→B, which is interpreted as a trade-off between minimizing the conservative action and maximizing path entropy production, i.e., a 'maximum entropy production principle (MaxEPP) for switching paths'. To obtain a criterion for relative stability of the two states, the authors introduce the approximation C_A→B ≈ C_B→A, which converts Eq. (19) into Eq. (20), an approximate proportionality between the difference of the minimum actions and the difference of the path entropy productions. The theory is tested numerically on the one-dimensional Schlögl model and the two-dimensional toggle switch model, using 100 random parameter sets for each: Fig. 3D reports strong linear correlations between action differences and path-entropy-production differences (r = 0.9445 and 1.0000), Figs.","tokens_in":10562,"tokens_out":30909,"duration_ms":288956,"significance":"The paper is a potentially useful contribution to stochastic thermodynamics and systems biology, provided the claims are properly qualified. The decomposition behind Eq. (19) is parameter-free given the Langevin model, and the reformulation of the FW action in thermodynamic terms (conservative action versus path entropy production) is conceptually attractive. The main strengths are the systematic numerical protocol — 100 random parameter sets per model with Gillespie simulations and geometric minimum-action path calculations — and the honest reporting of the failure statistics for the central approximation. The near-perfect linear relation in Fig. 3D, if confirmed with the fitted slope reported, would give practitioners a practical shortcut for estimating relative stability from path dissipation. On the critical side, the paper's primary novelty claim is partly a relabeling: Eq. (19) is an identity, and the falsifiable content lives in Eq. (20), whose validity is restricted by the C_A→B ≈ C_B→A approximation and its documented 10% failure rate.","major_comments":[{"comment":"The paper presents Eq. (19) as the derivation of a 'maximum entropy production principle for switching paths', but the decomposition ΩA = C − (1/2)ΔS_L is an algebraic identity given the definitions in Eqs. (7), (8), and (18); substituting Eq. (18) into Eq. (19) reproduces the expanded action term by term, so maximizing ΔS_L at fixed C is exactly equivalent to minimizing the FW action. Eq. (19) is therefore a rearrangement of the least-action principle rather than an independent derivation of a maximum principle. The reformulation may still be useful, but the paper should state this explicitly and locate the novel, falsifiable content in Eq. (20) and its numerical support; as written, the 'primary conclusion' overstates the status of Eq. (19).","section":"Section III, Eq. (19); Discussion, first paragraph"},{"comment":"The reduced MaxEPP statement — that more dissipative switches are exponentially more probable and that the relative stability of A versus B is governed by the difference in path entropy production — rests on the approximation C_A→B ≈ C_B→A that converts Eq. (19) into Eq. (20). The manuscript reports that this approximation holds for only 90% of the toggle-switch parameterizations and that 'significant divergence from the relation was generally observed in cases where the saddle point occurred at a low copy number compared to the steady states'. Since C_A→B − C_B→A is an O(Ω) quantity in the large-Ω limit, the divergence for the excluded parameter sets is not a finite-volume artifact and contributes to ln(k_A→B/k_B→A) at the same exponential order as the path-entropy-production difference. For those parameter sets, relative stability is therefore not determined by path entropy production alone, and the unqualified claims in the Abstract ('the entropy production during switching is key') and in the Discussion ('for sufficiently large volumes switches that produce more entropy will be favoured') overreach. The Discussion's secondary conclusion is already appropriately qualified, but the headline claims should be made explicitly conditional on the conservative-action approximation, or the failure regime should be characterized further (for example, by testing whether the 10% failure set persists and how it scales with Ω).","section":"Section III, paragraph after Eq. (19); Abstract; Discussion"},{"comment":"The numerical support for the central quantitative relation is reported only as Pearson correlation coefficients (r = 0.9445 for the toggle switch and r = 1.0000 for the Schlögl model). Eq. (20) predicts a specific linear relation with a definite slope (including the factor 1/2 and a definite sign), so the fitted slope and intercept with confidence intervals should be reported, and the roughly 90% of parameter sets where the approximation holds should be analyzed separately from the divergent ones. A high correlation alone does not establish the quantitative form of Eq. (20), which is the paper's main predictive statement.","section":"Section III, Fig. 3D and Eq. (20)"}],"minor_comments":[{"comment":"The chain of statements 'k_A→B = k_B→A' and 'k_A→B/k_B→A = exp(ΔS_L_{A→B})' is mutually inconsistent unless ΔS_L_{A→B} = 0, which would contradict the nonzero equal-and-opposite path entropy productions shown for the Schlögl model in Fig. 2C. Please clarify whether the ratio in Eq. (11) compares the switching rate with the rate of the time-reversed path ensemble (k̄_A→B) or with the reverse-switching rate (k_B→A), and correct the corresponding sentence.","section":"Section II.B, Eq. (11)"},{"comment":"The claim that the boundary term ⟨ln(P(X0)/P(XN))⟩ in Eq. (2) 'becomes negligibly small' in the large-Ω limit is not justified as stated; the logarithms of the stationary probabilities at the two macrostates generally differ by an O(Ω) amount in the WKB regime, the same order as the medium term. This statement should be derived or rephrased.","section":"Section II.A, after Eq. (2)"},{"comment":"The sentence 'the Langevin formalism within the steady state is equivalent to a quasi-equilibrium' is a strong interpretive claim that appears to conflict with the nonzero steady-state entropy production computed for the same models (Fig. 3A) and with the authors' own EP/EF decomposition (Figs. 2E and 2F); it should be softened or justified.","section":"Section II.B, after Eq. (8)"},{"comment":"Please report the values of Ω used for the simulations underlying Figs. 3B and 3D and state the range of action values sampled; the text notes that the results in Fig. 3B are coarsely discretized because a low Ω was used, and the reader needs this context to judge the large-volume relevance of the comparisons.","section":"Fig. 3"},{"comment":"The bars denoting time-reversed quantities are not rendered reliably in the text (for example, 'ln(WΓ/WΓ)' and 'kA→B/kA→B' in the paragraph after Eq. (2)); please fix the typography so the forward and time-reversed rates are clearly distinguishable.","section":"Section II.A, notation"},{"comment":"Eqs. (8) and the action split leading to Eq. (19) are attributed to the authors' own earlier work (ref. 31, Endres 2017); the text should state explicitly which results are new to this paper so that the incremental contribution is clear.","section":"References, novelty relative to ref. 31"}],"recommendation":"major_revision","confidential_remarks":"This is a competent paper whose central claims are, after reframing, defensible. The main point I would ask the editor to keep in mind is novelty disclosure relative to the authors' own ref. 31 (Endres, Sci. Rep. 2017), from which Eqs. (8) and the action split are taken; the present manuscript should be asked to delineate the incremental contribution explicitly. The paper fits the journal's scope in stochastic thermodynamics and biophysics. I do not see grounds for rejection, but the headline claims need the conditionalization described in major comment 2."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, honest stochastic thermodynamics paper. What's actually new is Eq. 20, an approximate relation between action differences and path entropy production differences, backed by systematic numerics on 100 random parameter sets for two models. The earlier Eq. 19 is a definitional split of the Freidlin–Wentzell action into a conservative part and half the path entropy production; it's exact but it's an identity, not a derivation of MaxEPP. The paper doesn't hide this, and the numerical support for Eq. 20 is real (correlations ~0.95 and 1.0). The models are standard but the random parameter sweep is a plus.\n\nSoft spots: first, the load-bearing approximation CA→B ≈ CB→A holds for only 90% of toggle switch parameterizations, as the authors admit. That is not a finite-volume artifact; it's a property of the force landscape. So the claim that 'more dissipative switches are more probable' is conditional, not universal. The abstract and discussion state it more generally than the caveat supports, though the body flags the failure mode (low-copy-number saddles). Second, the 1D argument has a consistency slip: they say kA→B = kB→A and then write kA→B/kB→A = exp(ΔS_L^A→B), which would force ΔS = 0. I think they mean something more subtle, but as written it's confusing and should be fixed. Third, the claim that steady-state entropy production plays no role is supported by a weak correlation (Fig. 3A), not by a scaling argument. That's fine as numerical evidence, but the abstract's tone outstrips it.\n\nWho this is for: people working on stochastic thermodynamics of gene regulatory or ecological switches. It deserves serious refereeing: the numerics are reproducible-looking, the derivation is clear, and the limitations are mostly stated. I'd send it to review but ask for the universal claim to be tamed and the 1D paragraph cleaned up.","headline":"A solid, honest stochastic thermodynamics paper whose genuinely new relation (Eq. 20) is supported by systematic numerics, but whose headline MaxEPP claim is conditional on an approximation that fails for ~10% of toggle switch parameterizations.","tokens_in":11072,"tokens_out":2706,"would_cite":true,"duration_ms":26680,"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":"Switching in multistable systems is governed by the entropy produced along the switching path, not by steady-state entropy.","keywords":["stochastic thermodynamics","entropy production","multistability","Freidlin-Wentzell action","Langevin dynamics","maximum entropy production principle","bistable models","state switching"],"falsifier":"Construct a two-dimensional multistable system whose saddle point is at low copy number, compute the forward and reverse minimum actions and path entropy productions, and test whether $\\frac{1}{2}(\\Delta S^{L}_{B\\to A} - \\Delta S^{L}_{A\\to B}) = \\Omega(\\mathcal{A}_{A\\to B} - \\mathcal{A}_{B\\to A})$; a clear violation in a slowly varying force regime would falsify the claimed universality.","tokens_in":10124,"feed_emoji":"🔀","tokens_out":10586,"duration_ms":89883,"temperature":0.7,"pith_summary":"This paper asks what sets the rates at which a multistable system switches between its stable states, far from equilibrium. By combining the fluctuation theorem for entropy along trajectories with the Freidlin–Wentzell least-action principle, the authors argue that in the large-volume limit the switching probability is controlled by the entropy produced along the switching path, not by steady-state entropy production or state entropy. Concretely, they derive a probability $P_{A\\to B}\\propto \\exp(\\Delta S^{L}_{A\\to B}/2 - C_{A\\to B})$ for the most probable switching path and verify on the Schlögl and toggle-switch models that differences in path entropy production track differences in action. If right, this gives a thermodynamic rule for relative stability: more dissipative switches are exponentially more probable, extending the spontaneous-reaction rule to switching in biological, ecological, and climate multistable systems.","feed_headline":"Switching between states is driven by path entropy, not steady-state entropy","feed_subtitle":"The more dissipative the switch, the more probable it is; steady-state entropy plays no role in stability.","key_machinery":"The load-bearing object is the Freidlin–Wentzell action $\\mathcal{A}[x] = \\frac{1}{2}\\int_0^\\tau (\\dot{x} - f)^{T} D^{-1} (\\dot{x} - f)\\, dt$, which assigns an exponential cost to switching paths in the large-volume limit. The paper splits this action as $\\Omega \\mathcal{A}_{A\\to B} = C_{A\\to B} - \\frac{1}{2}\\Delta S^{L}_{A\\to B}$, identifying the dissipative part with the entropy produced along the path, and uses the identity that every point of a minimum-action path has equal kinetic and potential contributions to justify $C_{A\\to B}\\approx C_{B\\to A}$. This decomposition, together with the fluctuation theorem for Langevin paths, converts the action-minimization problem into a statement about entropy production, yielding Eq. (19) and the relation $\\frac{1}{2}(\\Delta S^{L}_{B\\to A} - \\Delta S^{L}_{A\\to B}) \\approx \\Omega(\\mathcal{A}_{A\\to B} - \\mathcal{A}_{B\\to A})$.","core_discovery":"The central claim is that a reduced maximum-entropy-production principle holds for switching paths in the large volume limit: the probability of the most probable path from macrostate A to macrostate B is $P_{A\\to B} = \\exp(\\Delta S^{L}_{A\\to B}/2 - C_{A\\to B})/Q_{A\\to B}$, where $\\Delta S^{L}$ is the entropy produced along the path and $C$ is a conservative action that penalizes deviations from the deterministic dynamics. Because the conservative actions of the two opposite switching paths are nearly equal when the deterministic force varies slowly, the difference in action between A$\\to$B and B$\\to$A is set by the difference in path entropy production. The paper demonstrates on random parameterizations of two bistable models that this linear relation holds, that state entropy and diffusive noise strength have negligible effect on stability, and that steady-state entropy production shows only a weak correlation with occupation probabilities. The authors state the primary conclusion as extending the rule that exergonic reactions occur spontaneously to switching in multistable systems.","pith_inferences":["Eq. (20) could be used as a diagnostic on single-molecule data: forward and reverse switching rates together with per-path entropy measurements should obey the relation in slowly-varying-force regimes, and the first violations would pinpoint low-copy-number saddles where the reduced MaxEPP fails.","The same least-action plus entropy-production argument should extend to non-chemical multistable systems, such as ecological or climate models written as Langevin dynamics, predicting that basins reachable by more dissipative transitions are the more stable ones; this is a testable extension the paper does not carry out.","Should the action split generalize to spatially extended systems, relative stability of multiple coexisting attractors could be inferred from path entropy production alone, bypassing explicit minimization of the action."],"forward_implications":["In a bistable chemical system at large volume, the ratio of occupation probabilities is fixed by the minimum-action difference, which equals half the difference in path entropy productions; steady-state entropy production and state entropy can be dropped from the stability calculation.","Switches that produce more entropy along the path are exponentially more likely, so in a system with many macrostates the most dissipative transitions dominate at sufficiently large volume.","For one-dimensional systems, forward and reverse switching paths are time-reverses of each other, so the two switching rates are equal and the rate ratio is determined solely by the path entropy production.","The theory identifies when the simple rule breaks down: when the saddle point sits at low copy number, the conservative actions of opposite paths diverge and the clean relation between action differences and path entropy production no longer holds."],"supporting_citations":[{"why":"Supplies the Freidlin–Wentzell action functional used to compute switching-path probabilities.","marker":"[28]"},{"why":"Gives the decomposition of the action into conservative and dissipative parts that underlies Eq. (19).","marker":"[31]"},{"why":"Establishes the fluctuation theorem relating path probabilities to entropy production along trajectories.","marker":"[4]"},{"why":"Derives the chemical Fokker–Planck equation used for the Langevin coarse-graining of the master equation.","marker":"[22]"},{"why":"Provides the geometric minimum action method used to find the minimum-action switching paths in both models.","marker":"[35]"},{"why":"Defines the Schlögl model, one of the two bistable systems used to test the relations.","marker":"[13]"},{"why":"Defines the toggle switch model, the two-dimensional test system for the action-entropy relation.","marker":"[16]"},{"why":"Gives the method for computing steady-state entropy production, the quantity shown to be negligible for stability.","marker":"[37]"}],"fun_headline_variants":["Path entropy, not steady-state entropy, sets switching odds","Dissipation during switch, not steady state, decides stability","Switching follows path entropy production, ignores steady-state","Stability in multistable systems: path entropy over steady-state","Switch probability from path entropy, not system entropy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reduced maximum-entropy-production relation rests on the approximation that the two opposite switching paths have nearly equal conservative actions; the paper finds this holds for 90% of its toggle-switch parameter sets but fails when the saddle point is at low copy number.","fun_headline_variants_meta":{"raw":{"variants":["Path entropy, not steady-state entropy, sets switching odds","Dissipation during switch, not steady state, decides stability","Switching follows path entropy production, ignores steady-state","Stability in multistable systems: path entropy over steady-state","Switch probability from path entropy, not system entropy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000266,"raw_usage":{"total_tokens":1577,"prompt_tokens":876,"completion_tokens":701,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":492,"completion_tokens_details":{"reasoning_tokens":621}},"tokens_in":492,"tokens_out":701,"duration_ms":6807,"temperature":1.0,"reasoning_tokens":621,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:20:09.884853+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a two-dimensional multistable system whose saddle point is at low copy number, compute the forward and reverse minimum actions and path entropy productions, and test whether $\\frac{1}{2}(\\Delta S^{L}_{B\\to A} - \\Delta S^{L}_{A\\to B}) = \\Omega(\\mathcal{A}_{A\\to B} - \\mathcal{A}_{B\\to A})$; a clear violation in a slowly varying force regime would falsify the claimed universality.","supporting_citations":[{"cited_title":"Ventsel’ \\ and\\ author M.I","cited_arxiv_id":null,"evidence_quote":"Supplies the Freidlin–Wentzell action functional used to compute switching-path probabilities."},{"cited_title":"Endres ,\\ @noop journal journal Sci","cited_arxiv_id":null,"evidence_quote":"Gives the decomposition of the action into conservative and dissipative parts that underlies Eq. (19)."},{"cited_title":"Evans \\ and\\ author D.J","cited_arxiv_id":null,"evidence_quote":"Establishes the fluctuation theorem relating path probabilities to entropy production along trajectories."},{"cited_title":"Gillespie ,\\ @noop journal journal J","cited_arxiv_id":null,"evidence_quote":"Derives the chemical Fokker–Planck equation used for the Langevin coarse-graining of the master equation."},{"cited_title":"Heymann \\ and\\ author E","cited_arxiv_id":null,"evidence_quote":"Provides the geometric minimum action method used to find the minimum-action switching paths in both models."},{"cited_title":"Schl\\\"ogl ,\\ @noop journal journal Z","cited_arxiv_id":null,"evidence_quote":"Defines the Schlögl model, one of the two bistable systems used to test the relations."},{"cited_title":"Cherry \\ and\\ author F.R","cited_arxiv_id":null,"evidence_quote":"Defines the toggle switch model, the two-dimensional test system for the action-entropy relation."},{"cited_title":"Schnakenberg ,\\ @noop journal journal Rev","cited_arxiv_id":null,"evidence_quote":"Gives the method for computing steady-state entropy production, the quantity shown to be negligible for stability."}],"review_version":1}