Local Surrogates for Harmonic Vibrational Entropy in Multilattices

Harmonic vibrational entropy is a key finite-temperature contribution to defect thermodynamics, but direct evaluation by dense Hessian diagonalization scales cubically with atom count and is too costly for supercell convergence, migration-path sampling, and high-throughput defect studies. We develop local surrogate models for harmonic entropy in multilattices, including semiconductors, ordered alloys, and multispecies crystals with multi-atom bases and internal degrees of freedom. Unlike Bravais lattices, multilattices contain internal-shift degrees of freedom and optical phonon modes coupled to acoustic strain; entropy models must therefore resolve sublattice and species labels. For finite-range or screened atomistic models, we prove sublattice-resolved locality and cutoff-error estimates that justify replacing the global entropy calculation by a local, symmetry-respecting regression problem with controlled truncation error. This turns vibrational entropy from a global spectral calculation into a reusable local site model with linear evaluation cost at fixed cutoff. Numerical tests confirm the predicted locality behavior and show that sublattice/species-resolved surrogates achieve accurate regression, transfer across supercell sizes, and linear-scaling evaluation on Stillinger--Weber Si and CdTe benchmarks. The resulting method enables repeated harmonic-entropy evaluations in multispecies defect calculations while retaining explicit stability, truncation, and surrogate-error controls.