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LIT-521: Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states

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StatusActive — read in full 2026-10-02 (NOTE-426); worth reading as the founding attempt to derive the maximum-entropy-production principle (MaxEP) from Jaynes's maximum-entropy inference over microscopic paths, and as the source most later MEP work, Kleidon's included, cites for MEP's theoretical foundation. Read it as a programme, not a proof. The path distribution p_Γ ∝ exp(A_Γ) and its fluctuation theorem follow from the stated constraints. The MaxEP step needs a mean-field approximation and an assumption that the number of paths grows with their irreversible action, which is stated, not argued. The self-organized-criticality corollary is a mean-field artefact by Grinstein and Linsker's analysis (LIT-525), which this reading confirms.
Tagsthermodynamics, natural-sciences, information-theory, complex-systems, probabilistic-modeling
Cited as “paper” byNOTE-426 — Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
Cited as “source” byTHEORY-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, 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

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Roderick C. Dewar (2003), Journal of Physics A: Mathematical and General 36(3), 631–641 — DOI-10.1088/0305-4470/36/3/303 (preprint arXiv:cond-mat/0005382, 23 May 2000)

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 theoretical centre of MEP, the principle that a system with enough degrees of freedom settles into the steady state of greatest entropy production. That principle is the main rival in this literature to Prigogine’s minimum principle.

NOTE-426 is the close reading of 2026-10-02, and it placed the work: Active, as the reference for what the information-theoretic derivation of MEP is and where it is weak. Its status is contested, and the record should read it with its critics.

  • Grinstein and Linsker (LIT-525) show that its self-organized criticality (SOC) corollary rests on a mean-field approximation extended beyond its validity. They also show that the 2005 sequel’s far-from- equilibrium derivation of MaxEP holds only in the linear regime.
  • Kleidon’s review (LIT-519), which applies MEP to the Earth system, calls the foundation “still work in progress”.
  • Martyushev and Seleznev’s review (LIT-520), the main survey of the MEP literature, could not be read.

Two connections inside the record matter.

  • Upstream. The derivation inherits whatever standing Jaynes’s maximum-entropy inference has as a foundation of statistical mechanics. The Stanford Encyclopedia entry LIT-114 (read in NOTE-103) records that there is “no consensus on its significance, or even cogency”. NOTE-103’s “MEP” is the maximum-entropy principle, Jaynes’s, not maximum entropy production. The two acronyms collide, and this paper is where one is derived from the other.
  • Fluctuation theorem. The paper’s fluctuation theorem (Eq. 21) has the same form as the dynamical ones of Crooks (LIT-522) and Seifert’s review (LIT-523). Here it is a consequence of an inferred Gibbs-type path measure, not of a dynamics. NOTE-426 says why that difference matters.

On Prigogine: the paper’s only direct engagement is to recall Jaynes’s 1980 conjecture that Gibbs’s method is “closer in spirit to a principle of maximum entropy production” than to Prigogine’s minimum principle (p. 4). It does not argue against the minimum principle, and the 2005 sequel, by Grinstein and Linsker’s account, derives both principles from one condition.

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