nucleation

LIT-1897: Geometry of Nonequilibrium Reaction Networks

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StatusActive — read 2026-10-31 (NOTE-1476; appendices skimmed); worth reading for the cycle–cocycle geometry of reaction hypergraphs and as the exact form of the exchange's "a productive cycle need not be a stoichiometric cycle": catalysts cancel from the stoichiometric matrix, so mutual catalytic production is not a cycle of it (THEORY-1248).
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Tagsthermodynamics, mathematics
Cited as “paper” byNOTE-1476 — Dal Cengio, Lecomte & Polettini — Geometry of nonequilibrium reaction networks
Cited as “source” byTHEORY-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, 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

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Dal Cengio, S., Lecomte, V., & Polettini, M. (2023). Geometry of nonequilibrium reaction networks. Physical Review X, 13, 021040.

Read in NOTE-1476.

Why this is here

A13 §4 used it to separate three kinds of cycle that the exchange had run together: a production cycle among constraints, a stoichiometric cycle in the kernel of the reaction network, and a cycle in a sheaf’s kernel. “A productive cycle need not be a stoichiometric cycle.” The reading confirms this and makes it exact (THEORY-1248): the paper’s cycles are built from net stoichiometry, from which a catalyst cancels, so the mutual production that CLAIM-516 proves necessary is invisible to them and to the thermodynamic budget. In CASE-189 rewritten as chemistry, the stoichiometric cycles are the fuel-to-waste pathways. Its islands also give CLAIM-478 a chemical mechanism: a slowed reaction channel makes an approximate conservation law over the window the slowing opens.

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