  Previous heat capacity estimators used in path integral simulations either
have large variances that grow to infinity with the number of path variables or
require the evaluation of first and second order derivatives of the potential.
In the present paper, we show that the evaluation of the total energy by the
T-method estimator and of the heat capacity by the TT-method estimator can be
implemented by a finite difference scheme in a stable fashion. As such, the
variances of the resulting estimators are finite and the evaluation of the
estimators requires the potential function only. By comparison with the task of
computing the partition function, the evaluation of the estimators requires k +
1 times more calls to the potential, where k is the order of the difference
scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster
demonstrate that a second order central-difference scheme should suffice for
most applications.
