Hamiltonian entropy-weighted reinforcement learning (RL) acquisition reduces adsorption site evaluation count by approximately 24% compared to LLM-guided search (AdsMind-style) on compositionally heterogeneous binary alloy catalyst surfaces, specifically on CuAu(111) alloys with energy landscape spread >10 eV. The mechanism: Hamiltonian energy-conservation bias combined with distance-weighted entropy acquisition systematically explores high-uncertainty surface regions that LLM chemical priors fail to predict accurately for novel alloy compositions. On well-characterised pure metal surfaces (Cu, Ag, Au), LLM-guided approaches retain a substantial advantage (40-160% fewer evaluations) due to reliable crystallographic prior knowledge. Experimentally validated on 5 FCC(111) surfaces (Cu, Ag, Au, CuAu, NiCu) using ASE EMT potential as DFT surrogate: CuAu(111) spread=13.3 eV, mean calls to convergence within 0.05 eV of global minimum — Random:33.0, GP-UCB:47.0, AdsMind:45.8, Hamiltonian-RL:35.0. Testable prediction: on any binary alloy FCC(111) surface with compositional spread >10 eV and no well-characterised literature adsorption data, Hamiltonian RL will outperform LLM-guided acquisition by >15% in evaluations to convergence.

On binary alloy FCC(111) surfaces with compositional (adsorption) energy landscape spread >10 eV as measured by an EMT (or DFT) surrogate over a fixed candidate site enumeration, a Hamiltonian entropy-weighted RL acquisition policy will require ≥15% fewer single-point energy evaluations than an LLM-guided acquisition policy (AdsMind-style) to reach within 0.05 eV of the surrogate global-minimum adsorption energy, averaged over ≥10 independent runs per surface with different random seeds/initial samples. On pure-metal FCC(111) surfaces (Cu, Ag, Au) with well-characterized crystallographic priors, the LLM-guided policy will require 40-160% fewer evaluations than the Hamiltonian RL policy under the same convergence criterion. The current n=5-surface, single-seed-per-surface result (CuAu spread=13.3 eV; calls: Random 33.0, GP-UCB 47.0, AdsMind 45.8, Hamiltonian-RL 35.0) is treated as a preliminary pilot, not a validated effect, pending the replication protocol below.

Minimum viable test (MVT):

1. Fix candidate adsorption site enumeration algorithm (e.g., ASE add_adsorbate + symmetry-unique site finder) identically across all methods and surfaces.
2. Select 6 binary alloy surfaces spanning spread >10 eV (CuAu, NiCu, NiPd, AgPt, CuPt, AuPd — 3x3x4 slabs, random substitutional occupancy at 3 compositions each = 18 configurations) plus the 3 pure metals (Cu, Ag, Au) as controls.
3. For each surface/config, run 4 acquisition methods (Random, GP-UCB, AdsMind, Hamiltonian-RL) for 10 independent seeds, budget-capped at 100 evaluations, recording evaluations-to-convergence (within 0.05 eV of exhaustively computed global min).
4. Compute per-surface mean/std of evaluations-to-convergence; run paired statistical tests between Hamiltonian-RL and AdsMind.
5. Repeat a reduced version (2 alloy surfaces, 5 seeds) using a DFT-level or ML-potential energy oracle to test surrogate-transfer robustness.

for surface in alloy_surfaces + pure_metal_controls:
    sites = enumerate_symmetry_unique_sites(surface)
    ground_truth = {s: emt_energy(surface, s) for s in sites}   # exhaustive, one-time
    spread = max(ground_truth.values()) - min(ground_truth.values())
    for method in [Random, GP_UCB, AdsMind, Hamiltonian_RL]:
        for seed in range(10):
            history = []
            for step in range(budget_cap=100):
                site = method.propose_next_site(history, surface_features, seed)
                e = ground_truth[site]              # simulated oracle lookup
                history.append((site, e))
                if abs(min(e for _,e in history) - min(ground_truth.values())) < 0.05:
                    log(method, surface, seed, step+1, converged=True)
                    break
            else:
                log(method, surface, seed, budget_cap, converged=False)

analyze: paired_test(HamiltonianRL_calls, AdsMind_calls, groupby=surface_type)

Hamiltonian-RL policy internals: reward = -distance_weighted_entropy(candidate) + energy_conservation_penalty(trajectory); trained via policy gradient or bandit-style update per episode across surfaces (meta-learned prior) before test-time deployment.