Can the free energy steer the alloy search, and does it say anything new?

EXPERIMENTS.md · lines 1150–1197

E25 — The thermodynamics wired in as a generator objective

Date 2026-09-12 · Question Does the free energy actually work as a search objective, and does it say anything a cheap descriptor would not? · Provenance alloy_mogfn/surrogates/thermo.py (registered as ce_thermo), …/surrogate_test.py

Method. CEThermoSurrogate satisfies the existing Surrogate protocol, so the generator reaches it by name with no other change. It emits two objectives: free_energy at the calibration temperature, and solid_solution - the real configurational entropy as a fraction of the ideal value. The second is normally assumed to be 1; here it is measured, and it is not 1.

fit() is a deliberate no-op. A cluster expansion learns from energies of resolved occupancies; composition-level feedback carries no information about arrangement and cannot update it. Fitting a composition-level offset would leave every ranking unchanged while narrowing the reported uncertainty - worse than doing nothing.

Result. 1500 K, 64 occupancy samples, calibrated on 40 compositions:

The last row is the ensemble earning its place: the training structures were drawn near-equiatomic within whichever subset was chosen, so a 4:1 split sits at the edge of the sampled region and the bootstrap members disagree about it - a three-fold wider uncertainty, reported rather than discovered later. 100-125 compositions/s, with a cache that makes the generator's inevitable revisits free.

The two objectives are in tension, which is the finding. Over 200 compositions the correlation between free energy and entropy ratio is +0.670: since one is minimised and the other maximised, the alloys that lower their free energy most do it by ordering, which is exactly what stops them being random solid solutions. 16 of 200 sit on the Pareto front. A scalarised objective picks one of those 16 and never reports that the other 15 exist - which is the case for a multi-objective generator rather than a weighted sum, made on measurement instead of assertion.

Caveats. Two objectives is not yet a materials-design problem - nothing here says anything about strength, ductility or oxidation. It is the thermodynamic floor those would sit on. The design space's elements must be a subset of the expansion's; the adapter refuses otherwise rather than extrapolating to a species the expansion has no parameters for.