M. C. Cross, P. C. Hohenberg (1993), Reviews of Modern Physics 65(3):851–1112 — DOI-10.1103/RevModPhys.65.851
Key takeaways
- Spatial and temporal patterns in driven systems (convection, Taylor–Couette flow, chemical reactions, morphogenesis models, solidification, optics) can be classified by the linear instability of a uniform state, by its characteristic wave-number q₀ and frequency ω₀, and described near onset by universal amplitude equations.
- There is no free energy or other Lyapunov functional selecting non-equilibrium patterns in general. Variational descriptions are perturbative and valid only near threshold. The authors read this as a reason the field has had to proceed system by system.
- A closed chemical system, like a closed fluid, must come to equilibrium. Its non-equilibrium patterns are either transients or are sustained by external pumping.
Standing in the record
Filed on 2026-10-02 at the owner’s request, as the Rayleigh–Bénard entry among
the canonical systems of the dissipative-structure programme. The request
offered Bénard (1900) or a standard review and preferred this one if
readable. It was readable as an authors’ scan in the Caltech repository and
was chosen: it covers convection, Turing patterns (LIT-535) and the BZ
reaction (LIT-531) in one place, and corrects the usual story of
Bénard’s experiment. It is 262 pages, and only the sections the record needs
were read, so the NOTE is Skimmed.
Its bearing on the record:
- It is the main read check on the programme’s ambitions. Cross and Hohenberg use “dissipative structures” (citing Nicolis and Prigogine, LIT-524) only as one name, alongside “synergetics” and “self-organization”, for steady macroscopic structure under constant non-equilibrium conditions. Their conclusion (§XIII.B) quotes Glansdorff and Prigogine (LIT-537, p. 108) that “the search for a universal kinetic potential has proved to be unsuccessful”. It agrees with the Nobel lecture’s (LIT-516) own restriction of minimum entropy production to the strictly linear regime, and goes further: there is no global minimization principle for these structures at all beyond a perturbative one near threshold.
- The demarcation question in LIT-192, and LIT-211’s dissipative cluster. The authors end by doubting that structures “appearing from nowhere in a dissipative system” are yet a modelling first step toward “the emergence of life from the primordial soup” (p. 1080). The absence of a global principle is their reason. They allow, as “plausible … (although by no means demonstrated)”, that reaction–diffusion mechanisms may carry molecular information up to the cellular level. That is a physicist’s version of the point NOTE-094 records: pattern-forming physics is shared by organisms and non-organisms, and by itself says nothing about what makes the former special.
No instruction for machine-learning practice. The anthology does not hold it.