{"id":"e360163b-00c0-4e54-9579-d9c2a88105b4","arxiv_id":"2507.14294","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A thermodynamically consistent flocking model with explicit stored fuel shows active motion as a finite-lived transient between two equilibrium states.","lead":"Physicists add a finite fuel store to a standard model of moving, aligning particles, so the particles speed up while burning energy and settle back to a passive equilibrium when it runs out. The paper argues that such 'living' active states are generally transient interludes between two 'dead' equilibrium states.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The one-way fuel coupling in Eq. (3) is the load-bearing assumption: it makes the life-as-transient result follow by construction, and the concluding universality claim fails if mechanical feedback is added.","rationale":"Reader's weakest assumption is the same one I identify; I agree with that choice. I add that this is not merely a missing generalization: the mathematical statement of the final equilibrium, Eq. (8), relies on the fuel coordinate being a passive relaxation coordinate in H=U+Phi. With one-way coupling that relaxation is independent of the mechanical state, so the active phase is literally an externally imposed transient. The paper is explicit about this limitation at the passage following Eq. (3) and footnote [21], but the conclusion drops the qualification when it claims applicability to any Langevin-type active model. The proposed simulation would directly test whether a minimal feedback term changes the qualitative outcome; until then, the paper supports conditional acceptance of the specific model, not the universal life-death claim.","tokens_in":6897,"tokens_out":10950,"duration_ms":644647,"concrete_test":"Run the Fig. 3 simulations with Eq. (3) replaced by d n_i/dt = -k tanh(n_i) + lambda (1/N) sum_{j: r_ij<R} cos(theta_j - theta_i) for several lambda, including the aligned-manifold version d n_i/dt = -k tanh(n_i)(1 - mu (1/N) sum_j cos(theta_j - theta_i)) with mu=1, and compare <n(t)>, v_a(t), and depletion time to Fig. 3. If any positive-lambda run keeps <n> > 0 while v_a remains nonzero, or if mu=1 leaves an ordered state with finite fuel indefinitely, the 'transient life' conclusion is not robust to feedback. If all runs still relax to n=0 with the same phenomenology, the concern is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The decisive assumption is the one-way coupling introduced before Eq. (3): the fuel variables evolve independently of positions and orientations ('at first we will only consider ... but not vice-versa'). Because Eq. (3) contains no r_i or theta_i, n_i(t) is an autonomous stochastic process; the active force in Eq. (1) is therefore a pre-scheduled, decaying external drive. When n_i and dn_i/dt vanish, the mechanical system is passive and relaxes to the Boltzmann state e^{-U/Theta} used in Eq. (8). This makes 'death as true steady state and life as transient' a consequence of the construction, not of active-matter dynamics. The concluding claim that the framework applies to any Langevin-type active model requires feedback to be included; once fuel consumption depends on the mechanical state, the explicit steady state in Eq. (8) is no longer guaranteed and self-sustaining active states with residual fuel are not excluded. The paper's own caveat plus footnote [21] shows this is the point where the conclusion outruns the model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces a class of overdamped Langevin active-matter models with an explicit fuel variable n_i per particle. The mechanical degrees of freedom (positions and orientations) evolve under an aligning potential U, while the active self-propulsion term is proportional to dn_i/dt. Fuel dynamics is one-way: Eq. (3) is independent of positions and orientations. With the multiplicative noise choice A_i = 2ΘΓ_i, the authors write a Fokker–Planck equation and claim a Gibbs–Boltzmann steady state e^{-H/Θ}, where H=U+Φ. Simulations of a two-dimensional Vicsek-like flocking model show a disorder→order→disorder sequence as the fuel is consumed. The paper concludes that equilibrium (death) is the true steady state and that the active non-equilibrium state (life) is a transient between two equilibrium states, and claims the framework applies to any active model described by Langevin equations.","tokens_in":7164,"tokens_out":15352,"duration_ms":184700,"significance":"If correct, the paper would give a finite-fuel, thermodynamically consistent extension of standard active models and a concrete way to follow the onset and dissipation of activity. The Fokker–Planck steady-state calculation is standard and the simulations illustrate the intended disorder–order–disorder behavior. However, the main conceptual conclusion is substantially built into the model construction: the one-way fuel coupling and the choice of the active force make the passive endpoint a design feature rather than an emergent prediction. The claimed universality is not established. The paper is best viewed as a well-defined minimal model of finite-fuel activity, and its value would be clearer if the claims were narrowed accordingly.","major_comments":[{"comment":"The one-way coupling is load-bearing. Eq. (3) contains no dependence on r_i or θ_i, so the fuel variables evolve as an autonomous stochastic process and the active term -v0 u_i dn_i/dt in Eq. (1) is a pre-scheduled, decaying external drive. The conclusion that the active state is a transient between two equilibrium states is therefore a direct consequence of the model construction; the text itself says 'by definition' at the point where this is stated. The concluding claim that the framework can be applied to any active model described by Langevin equations is not supported: if fuel consumption depends on the mechanical variables, or if motion replenishes fuel, the monotonic depletion and the clean return to the passive equilibrium of Eq. (8) are not guaranteed. The caveat before Eq. (3) and footnote [21] acknowledge the restriction, but the conclusion does not.","section":"Model, Eq. (3)"},{"comment":"The active self-propulsion term is proportional to the total time derivative dn_i/dt, which includes the noise in Eq. (3). Even when n_i reaches the minimum of ϕ at n=0, the noise term in dn_i/dt is generically nonzero, so the active force does not strictly vanish when the fuel runs out. The statement that the active terms 'vanish when the fuel runs out' is only valid if the deterministic consumption rate -∂ϕ/∂n is used instead of the total derivative, or if n is absorbed at 0 with a reflecting boundary. Please clarify this point, as the passivity of the final state is central to the main conclusion.","section":"Eq. (1), model section"},{"comment":"The equilibrium end-state is put in by hand through the noise choice A=2ΘΓ and the fuel potential's minimum at n=0. This is a legitimate modeling choice, but it means that the identification 'equilibrium (death) is the true steady state' is not a nontrivial prediction of the dynamics. The paper should present these choices as the design mechanism responsible for the transient life/death behavior and should not present that behavior as an emergent property of active matter.","section":"Noise choice, Eq. (7)"}],"minor_comments":[{"comment":"The definition is written as v_a(t) ≡ ⟨|v_i(t)|⟩, but the right-hand side is |(1/N)∑ v_i|; the angle brackets and absolute value are in the wrong order. Please correct the notation.","section":"Eq. (10)"},{"comment":"The caption says 'Rescaled by the initial fuel potential Φ(n0)', but the panels show H, U and Φ; please state explicitly which normalization is used for each curve.","section":"Figure 3 caption"},{"comment":"The main text does not report the number of independent realizations or error bars for the ensemble averages in Fig. 4; please provide this information or state where it appears in the Supplementary Information.","section":"Figure 4"},{"comment":"The main text gives ζθ, ζ, ζn, R and J0, but omits the temperature Θ and the self-propulsion speed v0; these should be stated for reproducibility.","section":"Simulation parameters"},{"comment":"Reference [9] and reference [19] are the same Vicsek et al. paper; please cite it only once.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper would be stronger if reframed as a study of a restricted class of finite-fuel active models with one-way coupling. The current title and concluding paragraph overstate the scope, and the main conceptual claim is largely a consequence of the construction. With the claims narrowed and the active-force definition clarified, the manuscript could be a solid contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know up front. The paper is a genuinely useful template for finite-fuel active matter, and the simulations deliver the promised disorder-order-disorder arc. But the headline biological framing—'life as a transient between two deaths'—is baked into the construction, so the conceptual claim is weaker than the packaging.\n\nThe genuinely new piece is the stored-fuel variable n_i with its own potential Φ, and the active self-propulsion term proportional to -dn_i/dt. That is a clean way to make activity run down when fuel is exhausted, and it is a real departure from the usual infinite-reservoir assumption. The mathematical core is solid: the non-symmetric mobility matrix, the noise choice A = 2ΘΓ, and the Fokker-Planck reduction to a Boltzmann steady state when fuel is gone are standard but carefully assembled, and the positivity condition v0^2 < 4/(ζr ζn) is a nice concrete constraint. The simulations are illustrative and the phase portraits with color fading as fuel runs out are a good way to see the transient flocking.\n\nThe soft spots are real but mostly stem from the model's construction. Eq. (3) has no dependence on positions or orientations, so the fuel is an autonomous, pre-scheduled external drive. When n_i and dn_i/dt vanish, the mechanics is passive and relaxes to equilibrium by design. So the conclusion that equilibrium is the true steady state and activity is a transient is not an emergent finding; it is a consequence of the one-way coupling and the noise choice. The paper is honest about the one-way coupling at the outset and footnote [21] says generalization is possible, but the concluding claim that the framework applies to any Langevin-type active model overreaches. That would require fuel consumption to feed back on the mechanical state, and then the explicit Boltzmann steady state is no longer guaranteed. I'd also flag a small typo in the definition of v_a: the left side ⟨|v_i|⟩ is always 1 for unit directors; the intended quantity is clearly the magnitude of the ensemble average. Missing error bars in Figure 4 are a minor issue; the SI may cover it.\n\nWho is this for? Researchers who build models of catalytic colloids, bacteria consuming nutrients, or any energy-limited active system. They will get a useful starting template and a caution about how easily equilibrium endpoints can be inserted by hand. The paper deserves a serious referee; a careful revision should narrow the universality claim and fix the order-parameter definition.","headline":"A clean finite-fuel active matter template whose equilibrium endpoint is built in by construction; the useful physics is there, but the life-as-transient claim owes more to the setup than to emergent dynamics.","tokens_in":7651,"tokens_out":2977,"would_cite":true,"duration_ms":35383,"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":"Finite-fuel active matter settles into passive equilibrium; the active phase is a transient.","keywords":["active matter","finite fuel","Langevin dynamics","Vicsek model","flocking transition","non-equilibrium transient","thermodynamic consistency","fuel depletion"],"falsifier":"Simulate the same model with a fuel consumption rate that increases with local alignment; if the system still reaches the passive Gibbs distribution after the fuel is gone and shows no lingering order, the framework survives, whereas persisting order or a steady state that differs from $e^{-(U+\\Phi)/\\Theta}$ would falsify it.","tokens_in":6718,"feed_emoji":"🐦","tokens_out":9984,"duration_ms":105564,"temperature":0.7,"pith_summary":"The paper introduces active matter models that explicitly track stored energy—the 'fuel' that drives self-propulsion—instead of assuming an infinite energy reservoir. The authors aim to show that such finite-fuel systems are thermodynamically consistent and that their true steady state is a passive equilibrium; the ordered active phase is a possibly long-lived transient. Using a two-dimensional flocking model related to the Vicsek model, they show that a disordered passive system becomes an aligned flock while fuel lasts, then loses order and relaxes to equilibrium as fuel runs out. If correct, the result gives a general picture: activity in a closed finite-energy system is an episode, not a permanent state.","feed_headline":"Finite-fuel flocks relax to passive equilibrium","feed_subtitle":"A thermodynamically consistent flocking model tracks stored energy, so the active phase appears only as a transient.","key_machinery":"The central object is the non-symmetric mobility matrix $G_i$ that couples fuel consumption to self-propulsion in the Langevin equations. Choosing the noise covariance as $A_i = 2\\Theta\\Gamma_i$, where $\\Gamma_i$ is the symmetric part of $G_i$, makes the Fokker-Planck equation have a steady state $P \\propto e^{-H/\\Theta}$ with $H = U + \\Phi$, absorbing the fuel potential into an effective Hamiltonian. This choice is what gives the model thermodynamic consistency and gives the finite-fuel system a passive equilibrium endpoint.","core_discovery":"The authors claim that keeping track of stored energy turns the non-equilibrium active state into a transient: the full system's steady state is the equilibrium Gibbs-Boltzmann distribution $P_{\\mathrm{eq}} = Z^{-1} e^{-H/\\Theta}$ with $H = U + \\Phi$, where $U$ is the mechanical alignment potential and $\\Phi$ is the fuel potential. In their two-dimensional Vicsek-type flocking model, simulations show the order parameter rising from zero to a plateau while fuel is consumed, then decaying to zero when the fuel runs out, returning the system to a disordered passive equilibrium. The central discovery is that the active, ordered phase is a possibly long-lived transient between two equilibrium states.","pith_inferences":["The paper leaves open the reverse coupling in which mechanical motion changes fuel consumption; if that coupling is included, the monotonic fuel depletion and exact Gibbs-Boltzmann endpoint may fail, so the framework's boundary is a concrete next test.","Translated to the lab, a suspension of synthetic swimmers powered by a finite chemical reservoir should show an order parameter that rises, plateaus, and decays to zero on a timescale set by the fuel potential; measuring that curve would test the transient picture directly.","Applied to organisms that replenish their energy stores, the framework would need a term for fuel intake, which would likely replace the passive equilibrium endpoint with a sustained non-equilibrium cycle rather than a transient."],"forward_implications":["Any active model expressible as Langevin equations with explicit finite stored fuel should show the same disorder-order-disorder lifecycle as its fuel is consumed.","In a closed system, the ordered active state cannot be a true steady state; it lasts only while fuel is being converted into mechanical work.","The effective Hamiltonian $H = U + \\Phi$ provides a bookkeeping tool for tracking mechanical potential, fuel potential, and total energy through the active phase and its decay.","The fuel potential $\\phi(n)$ controls the duration and shape of the active transient, so different fuels yield different flocking lifetimes without changing the equilibrium endpoint."],"supporting_citations":[{"why":"The Vicsek flocking model that the finite-fuel model generalizes; supplies the aligning interaction and the order parameter.","marker":"[19]"},{"why":"A Vicsek-like model providing the order-disorder transition behavior used as the comparison point for the active steady state.","marker":"[20]"},{"why":"Supplies the stochastic calculus needed to map between Itô and Stratonovich discretizations of the multiplicative noise.","marker":"[22]"},{"why":"Supplies the Fokker-Planck formalism used to derive the steady-state distribution from the Langevin equations.","marker":"[23]"},{"why":"Cited as one of the results establishing the stable Gibbs-Boltzmann steady state of the Fokker-Planck equation.","marker":"[27]"},{"why":"Cited as another result establishing the steady-state distribution for the class of non-symmetric mobility models.","marker":"[28]"},{"why":"Provides the Euler-Maruyama integration scheme used for the numerical simulations.","marker":"[29]"}],"fun_headline_variants":["Fuel-burning flocks decay to passive equilibrium","Active flocks are transient guests of stored fuel","Finite fuel: order is only a transient","Stored energy makes active phase a fleeting state"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework assumes fuel is consumed at a rate that depends only on how much fuel remains, with particle motion and alignment never feeding back into the rate of fuel use; if that coupling is reversed, the clean return to passive equilibrium is no longer automatic.","fun_headline_variants_meta":{"raw":{"variants":["Fuel-burning flocks decay to passive equilibrium","Active flocks are transient guests of stored fuel","Finite fuel: order is only a transient","Stored energy makes active phase a fleeting state"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000476,"raw_usage":{"total_tokens":2251,"prompt_tokens":728,"completion_tokens":1523,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":344,"completion_tokens_details":{"reasoning_tokens":1466}},"tokens_in":344,"tokens_out":1523,"duration_ms":13470,"temperature":1.0,"reasoning_tokens":1466,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:00:11.892331+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the same model with a fuel consumption rate that increases with local alignment; if the system still reaches the passive Gibbs distribution after the fuel is gone and shows no lingering order, the framework survives, whereas persisting order or a steady state that differs from $e^{-(U+\\Phi)/\\Theta}$ would falsify it.","supporting_citations":[{"cited_title":"Chat´ e, F","cited_arxiv_id":null,"evidence_quote":"A Vicsek-like model providing the order-disorder transition behavior used as the comparison point for the active steady state."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the stochastic calculus needed to map between Itô and Stratonovich discretizations of the multiplicative noise."},{"cited_title":"Risken,The Fokker-Planck Equation(Springer: Berlin, 1984)","cited_arxiv_id":null,"evidence_quote":"Supplies the Fokker-Planck formalism used to derive the steady-state distribution from the Langevin equations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited as one of the results establishing the stable Gibbs-Boltzmann steady state of the Fokker-Planck equation."},{"cited_title":"An equation of state for active matter","cited_arxiv_id":"2201.10813","evidence_quote":"Cited as another result establishing the steady-state distribution for the class of non-symmetric mobility models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Euler-Maruyama integration scheme used for the numerical simulations."}],"review_version":1}