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LIT-525: Comments on a derivation and application of the ‘maximum entropy production’ principle

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StatusActive — read in full 2026-10-02 (NOTE-422); worth reading as the short, exact critique of Dewar's information-theoretic derivation of maximum entropy production. It shows that the 2005 derivation's key step holds only where the constitutive relations are linear, so MaxEP far from equilibrium is not established by it, and that the 2003 claim that MaxEP yields self-organized criticality is an artefact of a mean-field expansion. Read from the authors' submitted manuscript (Zenodo); the version of record was not seen. Its first point is checked here only on its own worked example, since Dewar 2005 itself could not be read.
Tagsthermodynamics, natural-sciences, information-theory, complex-systems
Cited as “paper” byNOTE-422 — Comments on a derivation and application of the ‘maximum entropy production’ principle
Cited as “source” byTHEORY-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

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G. Grinstein, R. Linsker (2007), Journal of Physics A: Mathematical and Theoretical 40(31), 9717–9720 (Comment) — DOI-10.1088/1751-8113/40/31/N01

Standing in the record

Filed on 2026-10-02 with the critics of Prigogine’s extremum principles and the maximum-entropy-production (MEP) literature, at the owner’s request to fill out the record’s coverage of dissipative structures. It is the record’s statement of why the information-theoretic foundation of MEP is not settled.

NOTE-422 is the close reading of 2026-10-02, and it placed the work: Active.

  • Second point, checked in full. It is correct against the paper it criticises, Dewar 2003 (LIT-521), which the record holds and has read. The SOC divergence there is produced by extending a quadratic expansion to all F.
  • First point, checked only on the authors’ own model. It concerns Dewar’s 2005 letter, which could not be read, so the record holds it on the strength of the spin chain. There λ(F) = τ artanh F and A(F)F = τF/(1 − F²) agree only as F → 0. The record is not filing Dewar 2005 because its text could not be reached.

Its scope is narrower than its reputation. It refutes one derivation of MaxEP, and one application. It says the existence of far-from-equilibrium extremal principles “has not been settled”. It does not say MaxEP is false, and it calls Dewar’s MaxEP–SOC conjecture “intuitively appealing”. Kleidon’s review (LIT-519) cites it as pointing out “some technical flaws in the derivation of the linkage of MEP and SOC”, which reports the second point and leaves out the first. The survey by Martyushev and Seleznev (LIT-520) predates it.

It bears on Prigogine’s minimum principle too. The same orthogonality condition gives both maximum and minimum dissipation in Dewar’s scheme. So the Comment’s conclusion, that the condition needs linear constitutive relations, applies to the minimum principle derived that way as well. In the Comment’s words, both derivations “do require ‘the usual near-equilibrium assumption of linear constitutive relations’”, the inner quotation being Dewar’s own phrase for what he claimed to avoid.

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