\(\displaystyle H(\mathbf{s}) \;=\; -\sum_i h_i s_i \;+\; \lambda \sum_{i<j} J_{ij}\, s_i s_j \;+\; H_{\mathrm{constraints}}\)

Each asset is a spin \(s_i \in \{0,1\}\): held or not held. Expected returns enter as local fields \(h_i\), the covariance matrix as pair couplings \(J_{ij}\), and portfolio rules (cardinality, sector exposure) as constraint terms. The optimal portfolio is the ground state of this Hamiltonian, located by simulated annealing: the system is cooled through a temperature schedule while the variational free energy is tracked. The constraint encoding and schedule used by the production engine are proprietary.