{"id":"e6c0e9ee-37c9-4a98-9972-fd900bee8b2c","arxiv_id":"2506.22017","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Ecosystems can be represented as circuits whose links grow with local energy dissipation, producing a sharp transition from collapse to a more complex, near-maximally dissipating state.","lead":"This paper builds a model in which ecosystems behave like electrical circuits whose connections strengthen or weaken based on the energy they dissipate. The model shows that such circuits suddenly switch from collapse to a self-sustaining, energy-dissipating state once the available energy crosses a threshold, which offers a physics-based explanation for how ecosystems and other living structures can spontaneously organize.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central phenomenology rests on Eq. (2)'s dissipation-driven growth rule; the Discussion concedes flux-based rules may be more appropriate for real ecosystems, but no test shows the phase transition survives such rules.","rationale":"The reader identified the adaptive rule in Eq. (2) as the weakest assumption; I agree. The paper's own Discussion concedes that flux-based growth rules may be more appropriate for ecosystems that divert substantial resource flux into biomass, and it does not test whether the central phase transition, save-the-weakest effect, or near-maximal dissipation survive under such rules. Since all conclusions are generated by this one rule, an untested biologically plausible alternative is a genuine load-bearing gap. However, the paper is a theoretical proposal, and the authors have been transparent about the modeling choices; the results are coherent within the stated model. Therefore the conditional verdict remains appropriate: accept the framework as a well-defined model, but do not yet claim ecosystem-level generality until the flux-based variant is tested. No change to the reader's verdict is needed.","tokens_in":23229,"tokens_out":12419,"duration_ms":132288,"concrete_test":"Simulate the same 10-node living circuits used in Figs. 2-4 (Appendix A parameters, sigma_maint=0.05, alpha=10^-4) but replace Eq. (2) with flux-based growth: dLambda_ij/dt = |J_ij| - sigma_maint*Lambda_ij, where J_ij = Lambda_ij(k_ij p_j - k_ji p_i). Sweep mu over the same range as Fig. 2c and measure: (i) whether a critical mu exists below which all edges collapse; (ii) whether a weakest edge with initial Lambda 10^3 lower is rescued; (iii) the ratio of steady-state dissipation to the global maximum. If any of these three outcomes differs qualitatively from the dissipation-driven results, the central claims are specific to the dissipation-based rule and the paper's ecosystem-level conclusions must be conditioned accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claims—a first-order transition from collapse to a dissipative NESS, save-the-weakest, and near-maximal dissipation—all follow from the adaptive rule in Eq. (2), dLambda_ij/dt = sigma_ij - sigma_maint*Lambda_ij. The logarithmic factor in sigma_ij (Eq. (3)) is what makes per-capita dissipation diverge as Lambda_ij -> 0, producing the rescue of weak edges and the threshold in Eq. (4). If growth were instead proportional to the net electron flux J_ij = Lambda_ij(k_ij p_j - k_ji p_i), the per-capita growth rate would be k_ij p_j - k_ji p_i, which does not diverge for small Lambda_ij. In that case, the non-monotonicity in Fig. 3b could vanish, and the first-order jump might become continuous or disappear. This is not a hypothetical objection: the Discussion explicitly states, 'in ecosystems where a substantial fraction of resource flux is diverted into biomass rather than energy dissipation, including flux-based local growth rules and more realistic redox chemistry, may be more appropriate. It would be interesting to see if global quantities like dissipation are still maximized in this context.' Thus the paper itself flags that a biologically relevant alternative growth rule is untested, and the ecosystem-level interpretation of the central results is therefore conditional on the dissipation-based rule.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces 'living circuits,' a mapping of microbial redox ecosystems onto electrical circuits whose edge conductances Λ_ij (species abundances) adapt according to dΛ_ij/dt = σ_ij − σ_maint Λ_ij, with σ_ij the thermodynamic dissipation on the edge (Eqs. 2–3). The authors report four main results: (i) a first-order phase transition from complete collapse to a dissipative nonequilibrium steady state (NESS) at a critical drive μ_crit satisfying (e^{μ_crit} − 1) μ_crit = σ_maint/χ(k) (Eq. 4); (ii) a 'save-the-weakest' feedback that rescues weak edges; (iii) near-maximal total dissipation reached without global optimization; and (iv) a drive-complexity relationship that saturates at ≈4/N for low-variance kinetics. Support comes from numerical integration of circuits with up to 10 nodes and 45 edges, analytic calculations for n-cycles (Appendices D–J), and an independently parameterized redox-tower model (Appendix C, Fig. S2).","tokens_in":23519,"tokens_out":28944,"duration_ms":294697,"significance":"If correct, the framework is a valuable contribution to nonequilibrium physics of adaptive systems: it provides a tractable model in which the system's distance from equilibrium is itself a dynamical variable, with concrete analytic predictions (Eq. 4; the 4/N complexity saturation; the two-battery phase diagrams) and a mechanism qualitatively opposite to the pruning rules of vascular and Physarum networks. Strengths of the manuscript include the explicit statement of approximations and free parameters, the clean threshold calculation for cycles (Appendix D), the consistency between random-k_ij and redox-tower parameterizations (Fig. S2), and the authors' candid identification of the model's limitations in the Discussion. The main limitation is that all central results are established for a single postulated growth rule, and the paper itself flags flux-based growth rules as more appropriate for many ecosystems; whether the phase transition, save-the-weakest, and near-maximal dissipation survive that change is untested. The quantitative near-optimality claim for complex circuits also depends on an incompletely documented global-maximization computation.","major_comments":[{"comment":"The ecosystem-level reading of the central results is conditioned on the dissipation-based growth rule of Eq. (2), and the Discussion explicitly concedes that for ecosystems in which a substantial fraction of resource flux is diverted into biomass, 'flux-based local growth rules and more realistic redox chemistry ... may be more appropriate.' No test is given for whether any of the four central claims survive a flux-based rule dΛ_ij/dt = J_ij − σ_maint Λ_ij. I note that the specific stress-test mechanism suggested in a skeptical reading — that the logarithmic factor in Eq. (3) makes per-capita dissipation σ_ij/Λ_ij diverge as Λ_ij → 0 — does not actually occur: σ_ij/Λ_ij = (k_ij p_j − k_ji p_i) log(k_ij p_j/k_ji p_i) stays finite in that limit because the quasi-steady-state p_i are set by the rest of the circuit. The non-monotonicity in Fig. 3b is therefore controlled by the flux per unit conductance, a quantity a flux-based rule also contains, so a threshold and a rescue mechanism may well survive. However, the near-maximal dissipation result (Eq. 6 and Appendix H) is derived specifically from the logarithmic dissipation structure, and it is not evident that a flux-based rule would maximize dissipation rather than total flux. I request either (a) a supplementary numerical test of the flux-based rule covering the claims of Figs. 2–5, or (b) a revision that explicitly conditions the Abstract's claim that the work 'establishes ecosystems as paradigmatic examples of living circuits' on the dissipation-based rule.","section":"Discussion; Eqs. (2)–(3), (6); Appendix H"},{"comment":"The near-maximal dissipation claim is quantified as '≈ 7x closer to the global maximum' (Fig. 4d) and 'much closer to the max than expected' (Fig. 4b). For the 10-node, 45-edge circuits, the global maximum is a constrained optimization problem over a ~45-dimensional conductance simplex, but the manuscript does not state how the blue histograms were computed — which optimizer, what multi-start strategy, what convergence tolerance, and how the authors verified that the computed value is the global rather than a local maximum. If the blue distribution is produced by a local optimizer, the near-optimality claim could be overstated or initialization-dependent. Please describe the optimization procedure; for the 3-node circuits (Fig. 4a) the exact maximum can be verified by grid search, and a similar verification on small N would establish the method's reliability.","section":"Fig. 4b,d; near-optimal dissipation section; Appendix H"},{"comment":"The first-order nature of the transition and the absence of hysteresis are central to the contrast with conventional nonequilibrium circuits. The discontinuity itself is well supported for cycles by the static existence calculation in Appendix E and by Fig. 2c. However, the claim of convergence from 'different initial conditions' to the same NESS (Fig. 2d) is reported without specifying the number or distribution of initial conditions, and the stability of the collapsed state for μ > μ_crit is not analyzed: Appendix E is a static search over the conductance simplex for configurations in which every edge's per-capita dissipation exceeds σ_maint, not a dynamical stability analysis of the collapse boundary. Since a discontinuous jump in the order parameter without a bistable window is an unusual and interesting feature, please report the tested ensemble and, at least for the 3-cycle, confirm analytically or numerically that the collapsed state is unstable for all μ > μ_crit.","section":"Fig. 2c,d; Appendix E"}],"minor_comments":[{"comment":"The displayed master equation dpi/dt = Σ_j W_ij p_j omits the loss term −Σ_j W_ji p_i; Appendix B writes the correct form, and the flux and dissipation formulas in Eqs. (3) and (A4) are consistent with the complete equation. Please correct the displayed equation in all three locations, since a reader reproducing the quasi-steady-state reduction in Appendix A would otherwise obtain the wrong starting point.","section":"Eq. (1); Eq. (A2); Eq. (E1)"},{"comment":"The construction of the detailed-balance rate matrix is incompletely specified: sampling 'the upper triangular part and the lower penultimate diagonal' does not determine a unique algorithm, and the Gaussian (mean 1, std 0.3) can draw negative rates. Please provide an explicit algorithm (e.g., sample node potentials and symmetric amplitudes, then set k_ij/k_ji = exp(q_j − q_i)) and state how negative draws are handled.","section":"Appendix A (Methods)"},{"comment":"No code or data availability statement is given, and the numbers of realizations and initial conditions are not reported for Figs. 2c, 2d, 4b–d, and 5b. Please add these details, preferably with a code repository, so the simulation claims can be independently verified.","section":"Reproducibility"},{"comment":"Eq. (4) relates μ_crit to the free maintenance parameter σ_maint; it is a threshold consistency condition rather than an ab initio prediction. The caption of Fig. 5b describes a '1-parameter fit to theoretical predictions' — please state which parameter is fitted and list explicitly which quantities are predicted versus fitted.","section":"Eq. (4); Fig. 5b"},{"comment":"The statement that the dynamics 'lack any obvious global optimization principles such as a Lyapunov function' should be reconciled with Eq. (6), which shows the ratio dynamics approximate gradient ascent on log σ_tot with a state-dependent metric; clarify whether the claim is that no exact Lyapunov function is known, since an approximate gradient structure is displayed.","section":"Appendix H"},{"comment":"Please define the 'typical dissipation' (green) sampling distribution — presumably uniformly random normalized conductances on the simplex — and state how many random configurations were drawn per realization.","section":"Fig. 4b,d"},{"comment":"The phrases 'exact mapping' and 'rigorously map' are stronger than what Appendix B establishes, given the linear-regime (Michaelis–Menten, substrate ≪ K_M) assumption and the arbitrary choices in Appendix C; please qualify the claim accordingly.","section":"Fig. 1 caption; Abstract"},{"comment":"The claim that the logistic cutoff α is inconsequential can be justified directly: the factor (1 − α Σ Λ) multiplies every dΛ_ij/dt by the same scalar, so on the simplex of conductance ratios it only reparameterizes time and does not shift the fixed points of the per-capita dissipation. Adding this one-line argument would remove the need for the reader to take the claim on faith.","section":"Appendix A (Eq. A5)"},{"comment":"Please fix the duplicated 'use use' in the section on nonequilibrium steady states and the garbled author names 'Pavsko vZupanovi´c' in refs. [47], [62], and [64].","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"For the editor: I have judged this as a theory paper without empirical validation. The core phenomenology is internally consistent and analytically supported for cycles. My main reservation is framing: the title and abstract claim ecosystem-level significance, while the robustness of the results to the class of biologically motivated growth rules is untested and partly disclaimed in the Discussion. If the authors decline to add the robustness check, the claims should be tempered or the article framed primarily as a physics-of-adaptive-networks contribution. No issues with novelty or citation practice."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi,\n\nThis is a theory paper worth taking seriously. It maps microbial redox networks to Markov chains with adaptive edge conductances, where each edge (species) grows proportionally to its thermodynamic dissipation minus a maintenance cost. From that single local rule the authors get a first-order phase transition to a nonequilibrium dissipative steady state, a 'save the weakest' feedback, near-maximal total dissipation, and drive-dependent complexity. The phase transition is the headline: ordinary fixed-drive nonequilibrium circuits dissipate for any nonzero drive, but these adaptive circuits collapse below a critical potential. That is a clean, nontrivial result.\n\nWhat's genuinely new is the contrast with earlier adaptive network models (Physarum, vascular, current-based rules) that minimize dissipation and prune weak links. Here each edge is a selfish agent paying its own maintenance, and the emergent behavior is the opposite. The paper also derives analytic results for cycles: the critical-drive formula, the approximate Lyapunov function near extinction, and the near-equivalence to gradient ascent on total dissipation. And it tests the core phenomena using redox-tower kinetics from real species, not just random rates. That is good work.\n\nThe soft spot is the load-bearing assumption: Eq. (2) is postulated, not derived from any population-dynamics model. Growth proportional to dissipation is plausible, but the Discussion openly says that flux-based growth rules may be more appropriate when much resource flux goes to biomass. The stress-test note claims that a flux-based rule would destroy the phase transition because per-capita dissipation would not diverge as lambda goes to zero. That specific mechanism is wrong: the paper's own Appendix D shows per-capita dissipation stays finite as an edge conductance goes to zero, because the logarithmic factor has no conductance in it. But the broader robustness question is real: no test shows the first-order transition or save-the-weakest survives alternative growth rules. A referee should ask for that analysis. Also, the 'exact mapping' phrasing overstates; it is exact only under linear, closed, single-path assumptions, and the paper should say so. There is no code or data deposited, which is a practical obstacle to checking the simulations.\n\nOverall, this is a solid model paper, honestly limited. The central physics holds for the stated model, and the ecosystem interpretation is conditional on the growth rule. I'd send it to peer review and ask for a robustness analysis and code release. It would be a good reading-group paper: people will argue about whether dissipation is the right currency.","headline":"Clean theory paper: adaptive dissipation gives a first-order transition to a dissipative state, but the central growth rule is postulated and the ecosystem interpretation is conditional on it.","tokens_in":24023,"tokens_out":4600,"would_cite":true,"duration_ms":52785,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["92D40","82C31"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that living circuits—adaptive networks that set their own energy coupling—switch abruptly from complete collapse to a functioning dissipative state once the driving potential crosses a critical threshold, in contrast to…","keywords":["living circuits","adaptive dissipation","nonequilibrium steady state","phase transition","microbial ecosystems","redox metabolism","save the weakest","maximum dissipation principle"],"falsifier":"A controlled experiment could settle the central rule directly: grow a defined microbial community on a redox pair with known potentials, measure each species' per-capita growth rate against the thermodynamic dissipation on its catalyzed edge across several driving potentials; if growth does not track dissipation, the model's mechanism fails. Alternatively, a closed community with known redox kinetics and maintenance cost that persists at a light drive below the $\\mu_{\\rm crit}$ computed from $(e^{\\mu_{\\rm crit}}-1)\\mu_{\\rm crit} = \\sigma_{\\rm maint}/\\chi(k)$ would falsify the predicted collapse threshold.","tokens_in":23040,"feed_emoji":"⚡","tokens_out":9249,"duration_ms":91031,"temperature":0.7,"pith_summary":"This paper sets out to show that adaptive systems—systems that control their own coupling to an energy source—cannot be described by the usual framework of driven nonequilibrium physics. Using microbial ecosystems as a model, the authors map the flow of electrons through redox metabolism onto an electrical circuit whose edge conductances are species abundances that grow with the energy they dissipate and decay with a maintenance cost. They find that such \"living circuits\" undergo a first-order phase transition: below a critical driving potential the circuit collapses to an equilibrium state with no dissipation, while above it the circuit jumps into a nonequilibrium steady state that dissipates energy. If this is right, ecosystems can switch abruptly from death to a functioning, energy-consuming state through purely local rules, and they may do so at near-maximal dissipation without any global objective.","feed_headline":"Ecosystems snap from collapse to function at a critical energy drive","feed_subtitle":"A living-circuit model gives a sharp start-up threshold, near-maximal dissipation, and rescue of weak species from local rules alone.","key_machinery":"The machinery is the mapping of a microbial ecosystem onto a Markov chain and electrical circuit, combined with the adaptive conductance rule $\\frac{d\\Lambda_{ij}}{dt} = \\sigma_{ij} - \\sigma_{\\rm maint}\\Lambda_{ij}$, where $\\sigma_{ij} = (W_{ij}p_j - W_{ji}p_i)\\log(W_{ij}p_j/W_{ji}p_i)$ is the dissipation on the edge and $\\sigma_{\\rm maint}$ is a fixed per-capita maintenance cost. Species abundances become edge conductances, the master equation for electron densities becomes Kirchhoff's current law, and autotrophs act as batteries that break detailed balance with driving potential $\\mu$. The load-bearing identity is the criticality condition $(e^{\\mu_{\\rm crit}}-1)\\cdot \\mu_{\\rm crit} = \\sigma_{\\rm maint}/\\chi(k)$, which ties the collapse threshold to the ratio of maintenance cost and an emergent chemical current. The \"save the weakest\" effect is carried by a quadratic effective potential for a weak edge, $d\\Lambda_{\\rm weak}/dt \\approx \\frac{d}{d\\Lambda_{\\rm weak}}(\\tfrac{1}{2}\\Xi_{\\rm eff}\\Lambda_{\\rm weak}^2)$, whose curvature changes sign precisely at the phase transition.","core_discovery":"On the paper's own terms, the central discovery is that a network whose links grow according to the local thermodynamic dissipation on each link—$\\frac{d\\Lambda_{ij}}{dt} = \\sigma_{ij} - \\sigma_{\\rm maint}\\Lambda_{ij}$—does not behave like an ordinary driven circuit. Unlike conventional nonequilibrium circuits, which dissipate for any nonzero drive, living circuits only sustain a nonequilibrium steady state beyond a critical driving potential $\\mu_{\\rm crit}$, obeying $(e^{\\mu_{\\rm crit}}-1)\\cdot \\mu_{\\rm crit} = \\sigma_{\\rm maint}/\\chi(k)$, where $\\chi(k)$ is an emergent current set by the redox kinetics. Right at the threshold the dissipation jumps discontinuously, signaling a first-order phase transition between complete collapse and a dissipative state in which every surviving edge dissipates more than its maintenance cost. The same local rule produces a \"save the weakest\" feedback that rescues nearly extinct edges by routing transient dissipation through them, drives the circuit to near-maximal total dissipation without any global optimization principle, and yields richer topologies at higher drive.","pith_inferences":["If real microbial growth follows biomass yield or cross-feeding fluxes instead of dissipation, the sharp phase transition and near-maximal dissipation could persist in modified form or disappear; a yield-based growth rule is the most direct stress test of the framework.","The $4/N$ saturation suggests a testable ecological prediction: a single dominant energy source can sustain at most a small fraction of possible metabolic strategies in a large community, so biodiversity should scale weakly with species pool size in energy-limited closed systems.","The same local rule could produce collapse-to-function transitions in other adaptive structures, such as neural networks with dissipation-driven synaptic plasticity; the paper motivates but does not test this generalization.","The explicit formula for $\\mu_{\\rm crit}$ could be used quantitatively: with measured redox potentials, maintenance costs, and light input, one could predict which Winogradsky columns or phototrophic mats should collapse versus persist."],"forward_implications":["Any closed ecosystem with insufficient energy input should collapse entirely to an equilibrium state of zero dissipation, rather than persisting at low activity.","Above the critical drive, surviving species dissipate more than their maintenance cost, and the final network topology is the same across initial conditions: different starting circuits converge to the same nonequilibrium steady state.","Because the weakest edges are transiently the most dissipative, near-extinct species can be rescued by community-level feedback, equalizing dissipation across species and stabilizing the community against perturbations.","Locally selfish, dissipation-seeking growth rules drive circuits to near-maximal total dissipation and, at higher drive, to more complex surviving topologies, with complexity saturating near $4/N$ for large single-battery circuits.","Multiple energy sources (autotrophs) can cooperate or compete depending on their placement, with cooperation being the typical case in random networks."],"supporting_citations":[{"why":"Supplies the ecological premise that closed ecosystems extract energy through self-organized nutrient cycles, motivating the dissipation-driven growth rule.","marker":"[39]"},{"why":"Provides the redox tower potentials and microbial-ecosystem background used to parametrize the kinetic rates $k_{ij}$.","marker":"[25]"},{"why":"Provides the \"follow the electron\" principle that the mapping extends from single species to whole ecosystems.","marker":"[27]"},{"why":"Supplies the network theory of master-equation systems used to represent the circuit and its dissipation.","marker":"[40]"},{"why":"Establishes the contrast: conventional driven chemical systems maintain nonequilibrium steady states for any nonzero drive, which living circuits violate.","marker":"[20]"},{"why":"Provides the contrasting adaptive-network rule (pruning weak links) that highlights the difference from \"save the weakest.\"","marker":"[42]"},{"why":"Frames the maximum entropy production principle for which the near-maximal dissipation result offers a mechanistic basis.","marker":"[46]"}],"fun_headline_variants":["Adaptive living circuits phase-transition at critical drive","Local rules rescue weak links and near-maximize dissipation","Ecosystems flip from dead to dissipative at a critical energy","First-order transition in adaptive driven networks","Living circuits: sharp start-up threshold from local rules"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results rest on the assumption that a species' abundance grows in proportion to the thermodynamic energy dissipated on the metabolic edge it catalyzes, minus a fixed per-capita maintenance cost; if real growth tracks biomass yield, resource concentration, or other fluxes instead of dissipation, the phase transition and its consequences could change or vanish.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive living circuits phase-transition at critical drive","Local rules rescue weak links and near-maximize dissipation","Ecosystems flip from dead to dissipative at a critical energy","First-order transition in adaptive driven networks","Living circuits: sharp start-up threshold from local rules"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00029,"raw_usage":{"total_tokens":1698,"prompt_tokens":949,"completion_tokens":749,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":565,"completion_tokens_details":{"reasoning_tokens":687}},"tokens_in":565,"tokens_out":749,"duration_ms":7894,"temperature":1.0,"reasoning_tokens":687,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:13:15.904410+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A controlled experiment could settle the central rule directly: grow a defined microbial community on a redox pair with known potentials, measure each species' per-capita growth rate against the thermodynamic dissipation on its catalyzed edge across several driving potentials; if growth does not track dissipation, the model's mechanism fails. Alternatively, a closed community with known redox kinetics and maintenance cost that persists at a light drive below the $\\mu_{\\rm crit}$ computed from $(e^{\\mu_{\\rm crit}}-1)\\mu_{\\rm crit} = \\sigma_{\\rm maint}/\\chi(k)$ would falsify the predicted collapse threshold.","supporting_citations":[{"cited_title":"Closed ecosystems extract energy through self-organized nutrient cycles","cited_arxiv_id":"2305.19102","evidence_quote":"Supplies the ecological premise that closed ecosystems extract energy through self-organized nutrient cycles, motivating the dissipation-driven growth rule."},{"cited_title":"Brock biology of microorganisms, volume 11","cited_arxiv_id":null,"evidence_quote":"Provides the redox tower potentials and microbial-ecosystem background used to parametrize the kinetic rates $k_{ij}$."},{"cited_title":"Introduction to a submolecular biology","cited_arxiv_id":null,"evidence_quote":"Provides the \"follow the electron\" principle that the mapping extends from single species to whole ecosystems."},{"cited_title":"Network theory of microscopic and macroscopic behavior of master equation systems","cited_arxiv_id":null,"evidence_quote":"Supplies the network theory of master-equation systems used to represent the circuit and its dissipation."},{"cited_title":"Phosphorylation energy hypothesis: open chemical systems and their biological functions","cited_arxiv_id":null,"evidence_quote":"Establishes the contrast: conventional driven chemical systems maintain nonequilibrium steady states for any nonzero drive, which living circuits violate."},{"cited_title":"Global op- timization, local adaptation, and the role of growth in distribution networks","cited_arxiv_id":null,"evidence_quote":"Provides the contrasting adaptive-network rule (pruning weak links) that highlights the difference from \"save the weakest.\""},{"cited_title":"Martyushev and Vladimir D","cited_arxiv_id":null,"evidence_quote":"Frames the maximum entropy production principle for which the near-maximal dissipation result offers a mechanistic basis."}],"review_version":1}