Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Thermodynamics — the second law and its extensions read for themselves — entropy and entropy production, irreversibility, nonequilibrium steady states and their stability, dissipative structures, fluctuation theorems and stochastic thermodynamics, and the thermodynamics of computation and of life (ADR-020).
34 of 1352 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-026 v4 | For a system driven without feedback through fixed kernels, the average work dissipated at each switch of the drive equals the memory that fails to predict the next input; that is nonnegative when the drive is Markov and, summed, bounds the protocol’s dissipation from below when each kernel keeps its equilibrium stationary, so there only nonpredictive memory is wasteful; with feedback, in one binary channel no predictive agent is efficient | Still, Sivak, Bell & Crooks (2012), LIT-327: β⟨W_diss⟩ for the switch x_t → x_{t+1} equals I[s_t;x_t] − I[s_t;x_{t+1}] (Eq. 14, an identity). Under a Markov drive this nostalgia is nonnegative, and summed it lower- bounds dissipation when each kernel keeps its equilibrium stationary; both conditions are unstated in the paper and derived here. Fiderer et al. (LIT-041) show that with feedback, in one binary channel, predictive, max-entropy-action and efficient agents are disjoint. The claim is an ensemble average, not a per-operation floor. Whether the bound fails without the two conditions is QUESTION-191. | Active |
| THEORY-030 v3 | For a memory evolving reversibly with its environment, Landauer’s bound prices only steps that lose logical distinguishability, at least k ln 2 of entropy per bit lost, exported to the environment and not necessarily as heat, so copying onto a blank register, measuring or evaluating a bit has no minimum cost; learning a label has a floor only in total entropy production, at least the information learnt, which in Goldt and Seifert’s perceptron can be paid in the weights’ own entropy with vanishing heat | Bennett (2003), LIT-360: the cost attaches to many-to-one maps of the logical state, at least k ln 2 of entropy per bit exported to non-information-bearing degrees of freedom, which “need not” be heat. The record derives it for a memory and environment evolving reversibly from an uncorrelated start: the environment’s entropy rises by at least the logical entropy lost, H(X | f(X)), and an injective step has no floor, attained exactly by a permutation. Goldt & Seifert (LIT-308) bound information learnt by total entropy production, payable with vanishing heat in their toy model. It does not license a k_BT ln 2 heat floor per judgment, per gradient step or per bit learnt. Whether the bound survives without reversible dynamics is QUESTION-215. | Active |
| THEORY-072 v4 | Organisms differ from dissipative structures such as a candle flame not by far-from-equilibrium self-maintenance, nor by circular self-maintenance alone, but by organisational differentiation: several distinct constraints that produce one another at different time scales | The record’s first answer to the demarcation question that NOTE-094 reports. Prigogine (LIT-516) supplies the dissipative structures, and nothing in his account separates them from organisms. Mossio, Saborido & Moreno (2009, LIT-570) grant a candle flame organisational closure. Its one macroscopic pattern keeps up the conditions of the combustion that makes it. They draw the line at organisational differentiation: in an organism several distinct structures make distinct contributions, where a flame makes “a unique contribution”. Montévil & Mossio (2015, LIT-582) narrow closure to mutual dependence among constraints. Each constraint must be both produced by and productive of another, with at least one slow and one fast dependence. On the record’s reading, that builds differentiation into closure, as Mossio and Bich (2014) already say of closure of constraints. No paper analyses a flame under the 2015 definitions. Neither paper says closure defines an organism. | Proposed |
| THEORY-209 v2 | A converged network trained with SGD is not at a point and does not sample its training loss: under a quadratic approximation it samples a Gibbs distribution on a modified loss, isotropic in the Hessian’s column space, with probability currents that keep it oscillating, so its speed and spread are set by the learning rate, momentum and batch size | Kunin et al. (2021), LIT-1011, read in NOTE-711. Modelled as an underdamped Langevin equation with noise covariance proportional to the Hessian, SGD at the end of training converges to a nonequilibrium stationary state: Gibbs on a modified loss whose curvature undoes the Hessian’s anisotropy, with inverse temperature S(1 − β²), in broken detailed balance. A ResNet-18 on ImageNet explores isotropically in a plane where the loss is anisotropic, oscillates at Hessian-dependent rates, and moves at the predicted speed across a hyperparameter sweep. For the learned-structure line, a trained solution is in part a property of the regime that trained it. Proposed: the deep-learning evidence is one network, under assumptions the paper concedes are strained. | Proposed |
| THEORY-211 v3 | In the stochastic-differential-equation model of SGD, with a gradient-noise covariance that depends on the parameters, minibatch noise drives the difference of squared norms along a rescaling symmetry, at a rate proportional to learning rate over batch size, to the point on the symmetry orbit where the gradient-noise traces of the two parameter groups are equal, whenever both groups carry noise; so at stationarity SGD neither keeps the difference fixed, as gradient flow does, nor lets it diffuse, as isotropic noise does, and differs from gradient descent by a finite amount however small the noise | Ziyin, Li & Ueda (LIT-1012, read in NOTE-714), with the gradient flow conservation law and the Itô term from Neural Mechanics (LIT-1013). If ℓ(u, w) = ℓ(λu, w/λ) for every sample, then under the SDE model of SGD d(‖u‖² − ‖w‖²)/dt = −T(uᵀC₁u − wᵀC₂w), with T = η/S. The noise has no component along the symmetry, but its dependence on the parameters produces a deterministic drift through Itô’s lemma. The drift points to the noise-balanced point, and weight decay adds to its rate. In a diagonal linear network the stationary distribution follows exactly: it is non-ergodic, has a memory of initialization, and collapses to zero above a critical temperature. The law is re-derived here (2026-10-19) within the SDE model; the tests are small synthetic networks, and whether it holds in deep networks on real data is QUESTION-164. | Active |
| THEORY-220 v3 | A far-from-equilibrium system that contributes to its own maintenance has functions relative to itself, with no history or observer needed, and one that switches among self-maintaining processes has indications of success that can be false by its own lights | Bickhard (2000), LIT-1029, read in NOTE-729. Function is contribution to a far-from-equilibrium system’s own persistence; the asymmetry between persisting and decaying gives function and dysfunction, always relative to the system served, so a parasite’s gut serves the parasite and harms the host. A candle flame has functions in this sense. Representation arrives with recursive self-maintenance: a system that picks its next interaction by how it has differentiated its environment implicitly predicates that the interaction will succeed, and can find the predication false. Proposed: a conceptual account, with no model, whose account of having a function (and so of malfunction) is deferred to another paper. | Proposed |
| THEORY-275 v5 | In two optically trapped beads with a symmetric hydrodynamic coupling, one trap moved by a recorded noise drive, time-delayed mutual information and transfer entropy follow the drive’s path rather than the coupling’s symmetry: the flow between the beads reads two-way under moderate drive, in experiment and numerics, and one-way under strong drive, in numerics of the fitted model only | Das, Manikandan and Banerjee (2025), LIT-947, read in NOTE-788. Two colloids are coupled by the fluid through a symmetric tensor, and recorded noise moves one trap. Time-delayed mutual information and transfer entropy give drive → driven → other, with backflow at moderate drive. In numerics only, flow is one-way at strong drive. With no drive the coupled particles are independent at steady state. The paper does not test an unrecorded drive shared by both units, and it does not claim that the measures reveal coupling architecture. Whether the same holds in other reciprocally coupled systems is QUESTION-186. | Active |
| THEORY-412 v2 | Driven matter tends toward states that look adapted to the drive, with no replication needed: of two outcomes of a system driven by a fixed external field, equal in internal entropy and in the probability of reversal, the likelier is the one whose formation absorbed work from the drive and dissipated it more reliably | Perunov, Marsland & England (2014; Phys. Rev. X 2016), LIT-518, read in NOTE-416, on England’s macrostate relation (LIT-515). The log-odds of two driven outcomes decompose exactly into an internal-entropy term, a reversal term and Ψ − Φ = −ln⟨e^{−βΔQ}⟩. The “tendency towards adaptation” needs the first two held equal. The paper does that only in two single-particle hopping models, argues the many-body case, and reports a driven-chemistry simulation without showing it. The reading judged the claim too weak to source a THEORY; it is filed as Proposed for that reason. “Adapted” here means absorbing the drive’s work, nothing more. | Proposed |
| THEORY-416 | Quantum thermodynamics has at least four inequivalent notions of work, the ensemble average, the two-point-measurement random variable, the ε-deterministic single-shot work content and the resource-theory work, which answer different operational questions; only the two single-shot optima coincide, by identification of formulas and for energy-diagonal states | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011. The review’s one synthesis (§5.2, §7) sets four definitions side by side: ⟨W⟩ = ∫tr[ρḢ]dt (Eq. 2), W = E_m^(τ) − E_n^(0) (Eq. 24), A^ε ≈ −kT ln(Z_Λ*/Z) (Eq. 49) and w^max_ε = F^min_ε(ρ_S) − F(τ_S) (Eq. 50). Only the last two agree, and that agreement is an observation that two published formulas match, for states diagonal in energy. It is an informed judgement of a 2016 snapshot, not a theorem that the notions cannot be unified. | Proposed |
| THEORY-431 | For classical systems with Markovian, microscopically reversible dynamics, the entropy production of a trajectory obeys an exact finite-time symmetry against the time-reversed process, P_F(+ω)/P_R(−ω) = e^ω, wherever ω is odd under reversal; Jarzynski’s work equality and the mean second law follow as corollaries, and the symmetry constrains fluctuations, not which steady state a system selects | Crooks (1999), LIT-522, read in NOTE-413, with Jarzynski (1997), LIT-517 (NOTE-417), and Seifert’s review (2012), LIT-523 (NOTE-420). The work equality ⟨e^{−βW}⟩ = e^{−βΔF} holds at any switching rate, and Crooks derives it from a trajectory-level entropy-production theorem; Seifert derives every known theorem of the kind from one master theorem. These are exact given their premises. They are not proofs of the second law, since the dynamics build irreversibility in, and they say nothing about extremum principles for steady states. Their practical reach is work fluctuations of order k_BT. | Active |
| THEORY-463 | In classical statistical mechanics a strictly irreversible approach to equilibrium cannot come from the isolated Hamiltonian dynamics alone: the fine-grained Gibbs entropy is constant and bounded systems recur, so each account surveyed either weakens the target to typical or long-run behaviour or adds something from outside the dynamics | Frigg & Werndl (2023), LIT-114, the SEP entry, read in NOTE-103. The impossibility half rests on standard consequences of Liouville’s theorem, time-reversal invariance and Poincaré recurrence. The classification half is the survey’s: it is stated account by account, not argued as a general result. The entry is classical only, excludes the direction of time, and reports rather than settles the disputes about each repair. | Active |
| THEORY-482 | For a closed quantum system that starts thermal and is measured projectively in energy before and after a unitary drive, the two-point-measurement work obeys the Jarzynski equality and the Tasaki–Crooks relation in exactly the classical form, because those energy measurements erase the coherences in which a quantum difference could appear | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011, which reproduces the derivation (Eqs. 24–30). With W_{m,n} = E_m^(τ) − E_n^(0), a thermal start and closed unitary evolution, ⟨e^{−βW}⟩ = e^{−βΔF} follows from Σ_n p_{m|n} = 1 (Eq. 29), identical in form to the classical relation. The identity is exact under its conditions. Its classicality is bought by the definition of work: two projective energy measurements destroy coherences, which is why the definition is contested. It says nothing about work defined without them. | Active |
| THEORY-492 | Life was forced into existence by geochemistry: core metabolism, rooted in the reductive citric-acid cycle, formed as a channel relieving the free-energy stresses abiotic processes keep building, as lightning relieves a charge separation, so its early steps would recur on any similar planet and selection on metabolism came before replication | Morowitz & Smith (2006 working paper; Complexity 2007), LIT-528, read in NOTE-425. An essay with no calculation, which says itself that the thesis “has not been quantitatively demonstrated”. Its evidence is the structure of present-day core metabolism, read back into its origin. Its framework is Jaynesian entropy maximization over states that include currents, and it rejects entropy-production principles. The reading judged that no THEORY was indicated; this one is filed as Proposed, a conjecture with a stated research programme. | Proposed |
| THEORY-513 | Observational entropy taken relative to a maximum-entropy prior τ, S(τ) − D_M(ρ‖τ), lies between S(ρ) and S(τ) for states meeting the prior’s constraint, is finite and continuous whenever S(τ) is, and reduces to about two dozen textbook entropies by choice of measurement and prior; its second laws are bounds on the time-averaged state’s divergence from the prior, proved small only under sufficient conditions (nondegenerate energy gaps for equilibration, the eigenstate thermalization hypothesis for fit to the prior) | Schindler, Strasberg, Galke, Winter & Jabbour (2025), LIT-082, read in full in NOTE-043, with Proofs 1, 2, 7, 10 and 11 checked line by line. The bounds, the special cases and the decomposition are proved. The central target, a small divergence of the time-averaged state from the prior, is proved for no concrete system; in the paper’s own examples “in none of those cases was the smallness proved here analytically” (p. 12). Unpublished as of the reading. | Active |
| THEORY-517 | Life raises the Earth’s entropy production, chiefly by increasing the absorption of sunlight, and if the planet is held at maximum entropy production, the negative feedbacks of that state would give the homeostasis the Gaia hypothesis postulates | Kleidon (2009), LIT-519, read in NOTE-423. The Earth’s entropy budget is dominated by the absorption of sunlight, and model studies, mostly the author’s, find that biotic activity raises it. The step to Gaia is explicitly conditional on MEP, which the same review says is not established, and its feedback argument is a schematic figure. It treats life as the most effective of the Earth’s dissipative processes, and gives no criterion separating a living dissipator from a convection cell. | Proposed |
| THEORY-532 | Systems pushed from equilibrium develop structures that degrade the applied gradient faster, and living systems and maturing ecosystems are such structures, continuous with convection cells and vortices, so the second law is a necessary but not a sufficient condition for life | Schneider & Kay (1994), LIT-533, read in NOTE-415. A “restated second law” (systems moved from equilibrium “utilize all avenues available to counter the applied gradients”) is offered as a corollary of Kestin’s equilibrium stability result and not derived from it. Bénard convection and a draining vortex show organized structures raising dissipation. One stressed marsh, airborne thermal scans and a satellite comparison are read as ecosystems developing to degrade more sunlight; all are correlational and confounded with water. The reading judged the claims too weak to source a THEORY; filed as Proposed. The paper itself says thermodynamics cannot tell the living from the non-living. | Proposed |
| THEORY-671 | An open system with enough internal degrees of freedom settles, among its possible steady states, into the one of maximum entropy production; this selects among steady states, where Prigogine’s minimum principle only describes relaxation toward one | Kleidon (2009), LIT-519, read in NOTE-423, states the principle and its Earth-system applications; Dewar (2003), LIT-521, read in NOTE-426, is the derivation it cites. The applications are model fits, mostly reported, many by the author. The derivation needs a mean-field step and an unargued assumption about path counts, and does not reach far from equilibrium (THEORY-676). “Sufficient degrees of freedom” is never made operational, so a failure can always be read as too few. The advocate’s own verdict: “no one would argue that MEP is well established”. | Proposed |
| THEORY-676 | Dewar’s information-theoretic derivation of maximum entropy production does not reach the far-from-equilibrium regime where the principle is applied: the 2003 route needs a mean-field step and an unargued assumption about path counts, the 2005 route’s orthogonality condition, which yields both maximum and minimum dissipation, holds only with linear constitutive relations, and the 2003 self-organized-criticality corollary is an artefact of a quadratic expansion | Grinstein & Linsker (2007), LIT-525, read in NOTE-422, against Dewar (2003), LIT-521, read in NOTE-426. The self-organized-criticality point was checked against Dewar 2003 and is correct. The linearity point concerns Dewar 2005, which the record could not read; it is held on the Comment’s account of its equations and on an exactly solvable spin chain, re-derived. The Comment removes one derivation and one application. It does not say MEP is false, and it says the existence of far-from-equilibrium extremal principles “has not been settled”. | Active |
| THEORY-679 | For dynamics obeying detailed balance in a heat bath, the heat released in a transition between observer-defined macrostates is bounded below by the log-odds against its reversal less the internal entropy change; where a replicator’s likeliest way back is a copy decaying within one generation, the bound grows with the copy’s durability and the speed of copying, not with the information copied | England (2012; J. Chem. Phys. 2013), LIT-515, read in NOTE-419. The general bound, β⟨ΔQ⟩ + ln π(II→I) + ΔS_int ≥ 0, is a coarse-grained second law and was re-derived. Applied to replication it gives a heat cost of about 2n ln(n τ_decay/τ_div) per copy, which falls away as division slows. The numbers for E. coli (within a factor of three of the bound) and RNA rest on an upper bound on the reverse probability that is argued from biology, not proved, and on an internal-entropy term set “arbitrarily”. It prices finite-time irreversibility, not information, and draws no line between living and non-living replicators. | Active |
| THEORY-692 | Near equilibrium, steady states minimise entropy production and every fluctuation decays; far from it, the excess entropy production has no fixed sign, so a fluctuation can grow past an instability of the thermodynamic branch into a structure held up only by flows across the boundary, and thermodynamics supplies only a sufficient condition for such a state’s stability, not a principle selecting which structure appears | Prigogine (1977), LIT-516, read in full in NOTE-424, with Cross & Hohenberg (1993), LIT-527, skimmed in NOTE-418. Minimum entropy production holds only for steady states in the strictly linear regime with constant coefficients. Beyond it, non-negative excess entropy production suffices for stability; its failure is not shown to give instability. Which structure appears is left to kinetics, boundaries and fluctuations. Cross and Hohenberg find no global minimisation principle beyond a perturbative one near threshold, and quote Glansdorff and Prigogine conceding that “the search for a universal kinetic potential has proved to be unsuccessful”. | Active |
| THEORY-779 | In Kunin et al.’s underdamped Langevin model of SGD with momentum on linear regression, with gradient-noise covariance σ²H independent of the parameters, the stationary state is Gaussian with parameter covariance ησ²H(H + λI)⁻¹/(2S(1 − β)) and velocity covariance σ²H/(S(1 − β²)): for small weight decay it spreads equally along every nonzero Hessian direction and not along the null space, each Hessian eigenmode is a damped oscillator with damping ratio (1 − β)/√(2η(1 + β)(ρ + λ)), and the expected squared step is η²σ² tr(H)/(S(1 − β²)) | Kunin et al. (2021), LIT-1011, §§4–6 and App. G, read in NOTE-711; the stationary moments re-derived by the promotion audit. An exact result for a model: Σ ∝ H constant and a quadratic loss are assumptions, and nothing here says a deep network meets them. The probability current is nonzero but reversible: under the model’s assumptions the stationary process is time-reversible once velocities are flipped, so it is “broken detailed balance” only in the paper’s sense, a nonzero current. | Active |
| THEORY-790 | In deep networks trained by SGD on real data, minibatch noise drives parameter groups related by a rescaling symmetry toward the point where their gradient noise balances, at a rate set by learning rate over batch size, so that at stationarity they sit neither where gradient flow would leave them nor spread out as under isotropic noise, as Ziyin, Li and Ueda propose | Ziyin, Li & Ueda, LIT-1012, read in NOTE-714, with the Itô term from LIT-1013. The law of balance is proved in the SDE model of SGD, and that part is the Active THEORY-211. The authors present the law as general to networks with rescaling symmetry, but test it only on small synthetic networks. This THEORY holds the general claim, for deep networks on real data, which no measurement in the record yet supports. | Proposed |
| THEORY-817 | Once an agent’s actions affect the percepts it receives, maximal prediction of those percepts is generally not what thermodynamic efficiency requires: in percept-action loops with feedback, maximally predictive agents generally extract less work than the most efficient agent | Fiderer et al. (2025), LIT-041, read in NOTE-032, prove that without feedback the work-efficient agents are exactly the maximally predictive ones that randomise and forget their actions, and that with feedback one binary memoryless channel separates predictive, max-entropy-action and efficient agents; from that they assert that with feedback maximally predictive agents are generally inefficient. The record holds as proved, in THEORY-026, only the one channel. It does not say that efficiency under feedback is a trade-off between prediction and forgetting: in the proved example the efficient agent is memoryless. | Proposed |
| THEORY-831 | For a system driven by a protocol fixed in advance, with microscopic reversibility and with forward and reverse processes started uniformly on their macrostates, the log-odds of two outcomes II and III reached from I equal the difference in their log state counts, plus the log-ratio of their reversal probabilities, plus the difference in minus the log mean of e^(−βQ) over the paths reaching each, where Q is the heat released; so when the first two terms are equal the likelier outcome is the one whose paths release more heat on average with less variation | Perunov, Marsland and England (2016), LIT-518, Eq. (8), read in full in NOTE-416 (which checked Eqs. 3–8), building on England’s macrostate relation (2013), LIT-515; re-derived by the promotion audit. An exact identity from microscopic reversibility, under a fixed protocol and uniform starting densities; the paper itself uses near-uniformity. It says nothing about which macrostates a real many-body system can be divided into with the other two terms equal. | Active |
| THEORY-1248 | Catalysts cancel out of the stoichiometric matrix, so a cycle of mutual catalytic production among species is not a stoichiometric cycle: the cycles that carry a reaction network’s steady currents and affinities are fuel-to-waste pathways through it, and who catalyses whom enters only the rates, never the thermodynamic driving | From the definitions of Dal Cengio, Lecomte and Polettini (2023), LIT-1897 (NOTE-1476), and Rao and Esposito (2016), LIT-1889 (NOTE-1464), neither of which says it in these words. It makes exact A13’s “a productive cycle need not be a stoichiometric cycle” from the exchange “Analyze nucleation concepts”. Checked on a reversible rewriting of CASE-189’s first construction. Active: definitional and checked. It does not say that catalytic cycles are thermodynamically idle. They decide which of the states the driving allows is reached, and bistability needs them; but the budget they work within is set elsewhere. | Active |
| THEORY-1250 | A chemostat is an emergent structure of a closed reaction network: when exchange reactions are fast and the reservoir species are abundant by a factor of order Omega, the closed network behaves to leading order as the open one, with its local detailed balance and dissipation, over a window that opens once exchange equilibrates and closes on a time of order Omega, after which a driven network relaxes to equilibrium; neither separation alone suffices | Remlein, Esposito and Avanzini (2026), LIT-1887, read in NOTE-1468: a multiscale expansion in the rate ratio ε and a WKB argument in the abundance ratio Ω, for arbitrary stoichiometry. The lifetime scaling was checked by integrating the paper’s §IX network, T_δ = 0.00483 Ω against its fit 0.0048 Ω + 0.33. Active. It does not say that every driven closed network departs from open behaviour at T ~ Ω, only that it can from then on, nor anything about systems that are not chemical. | Active |
| THEORY-1253 | Treating the Bayesian evidence as a partition function with sample size as inverse temperature, the analogue of heat capacity, the rate at which leave-one-out predictive loss falls with sample size, equals half the parameter count in a regular model, as equipartition, and the real log canonical threshold in a singular one, falling below these where prior or discreteness fixes parameters; with multiplicity above one the approach to the singular value is only logarithmic, and the correspondence has no counterpart of physical current or dissipation | LaMont & Wiggins (2019), LIT-1882, read in NOTE-1481: the learning capacity C = −N²∂_N U and its equipartition values (Table II, eqs. 16–18, 24, 28, 30). Active: the regular entries were checked by differentiation, and the singular case exactly in K = a²b² (CASE-152’s model), where C approaches λ = ½ as ½ − 1/log n, not with the O(1/N) error the paper states. The statistical “temperature” is a sample size, so nothing in the dictionary is a physical heat flow. | Active |
| THEORY-1261 | At stationarity a driven reaction network is confined to a thermodynamic space: each reaction’s affinity lies between zero and the largest cycle affinity per use of that reaction among the elementary flux modes containing it, and each product of concentrations lies between the effective equilibrium constants of the extremal pathways; with no driving the space collapses to the equilibrium point, so multistability, symmetry breaking and amplification above equilibrium need driving and are bounded by it | Liang, De Los Rios and Busiello (2024; PRX 2026), LIT-1886, read in NOTE-1463: eqs. 20, 24 and 29, proved for arbitrary stoichiometry from local detailed balance and the conformal decomposition of steady fluxes into elementary flux modes. Checked on the paper’s Schlögl parameters and on a reversible rewriting of CASE-189. Active. It bounds where a stationary state can be, for every choice of kinetics; it does not say which state is reached, whether it is stable, or how long the driving lasts. | Active |
| THEORY-1264 | Far from equilibrium, the weak-noise escape rate from an attractor goes as the exponential of minus system size times a barrier in the quasi-potential, not in any free energy, and that barrier is bracketed by thermodynamics: it is at most the entropy produced in relaxing from the saddle into the attractor and at least minus the entropy produced along the most likely escape path; the two bounds coincide at detailed balance and separate by twice the dissipation of the probability circulation, so far from equilibrium they can be very loose | Santolin, Freitas, Esposito & Falasco (2025), LIT-1881, read in NOTE-1465, for overdamped diffusions; Falasco & Esposito (2025), LIT-1892, §IV.H and appendix A, read in NOTE-1472, for jump processes with a macroscopic limit. Active: the derivation is two lines from the orthogonal decomposition of the drift and was checked on a linear nonequilibrium diffusion. It does not say that the more dissipative state lives longer, and in the one worked far-from-equilibrium chemical example the bracket is very loose. | Active |
| THEORY-1265 | Approximating a chemical master equation by a Fokker–Planck or nonlinear Langevin equation gets the quasi-potential right only at the fixed points: between them it mis-estimates the barriers, so escape rates come out wrong by a factor exponential in system size and the approximation can pick the wrong one of two states as the long-run favourite, and its apparent entropy production vanishes at every steady state, missing the dissipation that sustains it | Falasco & Esposito (2025), LIT-1892, §IV.D–E and §VII.A.1, read in NOTE-1472; Vellela & Qian (2009), LIT-1890, appendix A, read in NOTE-1474. Active: both formulas were checked on the Schlögl model, including Vellela & Qian’s counterexample, where the exact and diffusion quasi-potentials favour different states. It does not say diffusion approximations fail near fixed points or for Gaussian fluctuations; there they are exact to leading order. | Active |
| THEORY-1266 | In an open reaction network of reversible elementary mass-action reactions, sustained currents need an emergent cycle with nonzero affinity: each chemostatted species either breaks a conservation law or opens an emergent cycle, so one chemostat never suffices; with every emergent affinity zero the network relaxes to a unique equilibrium fixed by its unbroken conserved quantities; and a nonequilibrium steady state dissipates exactly the sum over emergent cycles of current times affinity | Rao and Esposito (2016), LIT-1889, read in NOTE-1464, with the one-chemostat proof of Dal Cengio, Lecomte and Polettini (2023), LIT-1897 (NOTE-1476). Active: rank–nullity, Wegscheider’s condition and two lines of algebra, checked numerically on a reversible rewriting of CASE-189’s first construction, which has a single equilibrium at zero affinity and is bistable only above 3.52 RT. It does not say that a driven network is far from equilibrium, multistable or organized; only that without an emergent affinity it cannot be, and what it costs when it is. | Active |
| THEORY-1268 | In a nonequilibrium steady state of a thermodynamically consistent Markov jump network, the entropy produced while a current is counted, times the squared relative uncertainty of that count, is at least 2k_B, independent of the counting time, so a current precise to ε costs at least 2k_BT/ε² of dissipation; the 2015 letter proves this within linear response and for single-cycle networks at any affinity, and for many-cycle networks far from equilibrium shows it numerically and states it as a conjecture | Barato & Seifert (2015), LIT-1885, read in full in NOTE-1480. Active for the scope stated in the title: the biased walk, the unicyclic formula (A/N) coth(A/2N) and the bound on random four-state networks were checked numerically. It bounds the precision of currents, not of occupations, so it does not price how long a maintained state lasts, and the general multicyclic proof is not in this paper. | Active |
| THEORY-1270 | Entropy production does not select which of several maintained steady states is the stable one: in the bistable Schlögl model the state the system occupies in the long run can carry either the higher or the lower deterministic entropy production rate, and the mean stochastic entropy production follows whichever state is more probable; in general the most dissipative attractor is the longest-lived only under special conditions, and lifetime tracks relaxation entropy only near detailed balance | Vellela & Qian (2009), LIT-1890 (§3.3, Fig. 6), read in NOTE-1474, show the counterexample; Falasco & Esposito (2025), LIT-1892 (§§III.F, IV.H, VIII.B.6), read in NOTE-1472, give the general account: minimum entropy production holds only near detailed balance with linear dynamics, and the two maximum principles hold only where relaxation and escape dissipations nearly coincide. Active as a negative result. It does not refute every extremum principle, only those that rank steady states by dissipation alone. | Active |
| THEORY-1273 | In a driven chemical system with two stable states and a finite number of molecules, each maintained state is metastable: it is left by fluctuation after a time exponential in system size, set by a barrier in a nonequilibrium quasi-potential that closes at the saddle-node, and the long-run share of time in each state is fixed by the parameters and system size, not by the initial condition; the deterministic rate equation, where the initial condition decides, holds only on times short of that escape time | Vellela & Qian (2009), LIT-1890, read in NOTE-1474, on the Schlögl model, with Falasco & Esposito’s general frame (LIT-1892, §§III.C, IV.H, VI; NOTE-1472). Active: the slow eigenvalue, the barriers, the initial-condition independence and the closing of the barrier at the fold were checked numerically on the paper’s model. It does not say which state is the more stable without computing the quasi-potential, and the paper’s own large-volume rate formula carries a spurious 1/V factor. | Active |