An improved thermodynamic energy estimator for path integral simulations

A new path integral energy estimator is presented that improves upon the thermodynamic energy estimator via a free particle projection. This centroid thermodynamic estimator significantly reduces the numerical noise of the thermodynamic estimator. The debate as to which estimator is better (virial, centroid virial, or thermodynamic) is partially resolved. The centroid estimators are found to be significantly better than their noncentroid analogues. The new centroid thermodynamic estimator has accuracy close to the centroid virial estimator, and may have particular advantages when derivatives of the potential are expensive to evaluate.