Source
Kleidon (2009), Naturwissenschaften 96:653–677, LIT-519, read in full in NOTE-423 from the open-access article (figure bodies lost, captions kept). Dewar (2003), J. Phys. A 36:631–641, LIT-521, read in full in NOTE-426 from arXiv v3, with the equation pages read as images. Martyushev and Seleznev’s review, to which Kleidon defers for MEP’s physical foundation, could not be read.
What was actually shown
The principle (LIT-519, p. 655). “If there are sufficient degrees of freedom within the system, it will adopt a steady state at which σ is maximized.” “Sufficient” is not defined.
Against Prigogine (LIT-519, pp. 655–656, 673). Prigogine’s principle “states that the steady state is one of minimum entropy production compared to transient states”; once a steady state is assumed it “makes no further predictions”. MEP “acts as a selection principle of the most probable out of many possible steady states”. The two are illustrated with box models (Figs. 1–2), not stated with their conditions (C1, moderate).
The flux–force trade-off. Where a flux depletes the gradient that drives it, entropy production is zero with no flux and zero with a flux strong enough to leave no gradient, so there is a maximum between. In a two-box model with alternative heat-loss paths, σ peaks at an intermediate conductivity (C2, strong for the existence of the maximum). Dewar’s two-box climate toy has its optimum at h_opt ≈ 0.199 f_SW, which NOTE-426 re-derived (0.1991).
The applications. Paltridge’s climate model and its successors, Mars and Titan, ocean steady states, mantle convection, evapotranspiration and sediment decomposition. In general-circulation sensitivity studies entropy production saturates at a maximum. Each is reported, not reproduced, and much of it is the author’s own model work.
The derivation (LIT-521). Maximize the entropy of the distribution over microscopic paths under fixed initial densities, fixed boundary fluxes and local conservation. Then p_Γ ∝ exp(A_Γ), with τσ_Γ/2k_B in the action (Eq. 14), and a fluctuation theorem and ⟨σ⟩ ≥ 0 follow exactly (Eqs. 18–21). MaxEP follows (Eqs. 22–24) only under a mean-field approximation and only if W(A^irr), the number of paths with irreversible action A^irr, increases with A^irr. That is assumed “with no argument or example” (NOTE-426; C3, weak). For climate, the quantity maximized is material, not radiative, entropy production (pp. 15–16), which answers Essex’s objection to Paltridge (C4, moderate).
What could have come out otherwise. The model fits could have missed, and the general-circulation runs could have shown no maximum. They did not. But no test fixed the degrees of freedom first, and the derivation offers no new prediction checked against data (NOTE-426).
What this does not say
- That MEP is established. “At this point, no one would argue that MEP is well established and that applications are without their limitations” (LIT-519, p. 673). The foundation is “still work in progress”.
- That it has been derived far from equilibrium. Dewar’s route needs the two assumptions above. His 2005 route, by Grinstein and Linsker’s analysis, holds only with linear constitutive relations, which is the regime where MEP would not differ from linear theory (THEORY-676). Kleidon’s review reports only the critique’s second point, about self-organized criticality, and leaves out this one (NOTE-423).
- That it can fail as stated. With “sufficient degrees of freedom” undefined, a non-MEP steady state can always be put down to too few (NOTE-423). Dewar’s version has the same escape: “When applications of the Jaynes procedure fail … [it] signals the presence of new constraints” (LIT-521, p. 6).
- That Prigogine’s principle is wrong. On this literature’s own account it answers another question. Prigogine’s own statement restricts the minimum theorem to the strictly linear regime (LIT-516).
- That maximum entropy production is Jaynes’s maximum entropy principle. The acronyms collide. Dewar derives the one from the other, and the cogency of Jaynes’s principle as a foundation of statistical mechanics is itself unsettled (LIT-114, NOTE-103).
- That it unites maximum power, the constructal law and self-organized criticality. Kleidon asserts it (C7). The link to self-organized criticality rests on Dewar’s 2003 corollary, which is a mean-field artefact.
Connections
- The critique (THEORY-676) is what blocks this account’s promotion by derivation.
- Pattern formation. Cross and Hohenberg (LIT-527) find “no evidence for the existence of any global minimization principles controlling the structure, except as a perturbative statement near threshold”. That is a claim about minimization functionals for patterns, not about entropy production, but it is the physicists’ standard caution against the programme.
- The rest of the dissipation literature. Schneider and Kay
(THEORY-532) and Morowitz and Smith (THEORY-492) both reject
entropy-production principles. Perunov, Marsland and England
(THEORY-412) say maximizing mean dissipation alone “is not predicted
to correspond to a likely outcome”. None of them argues it in a way the
record can check, so no
rivalsedge is declared. - The fluctuation theorems (THEORY-431). Dewar’s fluctuation theorem has the same form as Crooks’s, from an inferred path measure rather than a dynamics. The stochastic-thermodynamics framework uses no selection principle for steady states.
- Life and Gaia (THEORY-517) takes this account as its premise.
Note of 2026-10-29: what holds it back
Kept Proposed by the sixteenth status review. NOTE-423 and NOTE-426 read both sources in full, but neither result the promote_when asks for is in the record. Dewar’s derivation needs a mean-field step and an unargued assumption on path counts, and does not reach the far-from-equilibrium regime (THEORY-676, Active). No system has had its degrees of freedom fixed before its steady state was predicted and found. A split into what Kleidon proposes would free nothing: THEORY-517, which presupposes it, also asks for a planetary test that does not assume MEP.
Note of 2026-10-31: counterevidence from the Schlögl model
The readings of Vellela and Qian (LIT-1890) and of Falasco and Esposito (LIT-1892) bear against selection by maximum entropy production:
- in the bistable Schlögl model, the more stable state can carry either the higher or the lower entropy production (THEORY-1270);
- Falasco and Esposito find extremum principles hold only near detailed balance or under “peculiar conditions”.
A status review should weigh this. Nothing here changes its status.