On assessing the accuracy of defect free energy computations
Provides a theoretical foundation for error-controlled coarse-graining in defect free energy computations, relevant to materials science and statistical mechanics.
The paper develops a rigorous error analysis for coarse-graining of defect-formation free energy, establishing the thermodynamic limit and convergence rate for a 1D constrained atomistic system, and constructs coarse-grained energies with the same rate but reduced computational cost.
We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.