Calculation of thermodynamic properties using path integral Monte Carlo simulations in the canonical ensemble

The method of Lustig [J. Chem. Phys. 100, 3048-3059 (1994)] is applied to the path integral formulation of the quantum-mechanical canonical ensemble to derive equations for the calculation of all common thermodynamic properties in a rigorous and systematic way. Using these equations, thermodynamic properties such as the pressure, the isochoric and isobaric heat capacity, the speed of sound, or the Joule-Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations. The equations are derived for primitive and virial estimators. For the virial estimators, we generalize the finite-difference approach of Yamamoto [J. Chem. Phys. 123, 104101 (2005)] to arbitrary thermodynamic properties. We verify the derived equations by Monte Carlo simulations of supercritical helium-4 above the vapor-liquid critical point at selected state points on the 80 K isotherm using recent, highly accurate ab initio pair and nonadditive three-body potentials. The results of these simulations agree with our previous simulation results in the isobaric-isothermal ensemble, a virial equation of state of metrological quality, and the most accurate experimental data for the speed of sound in helium within their mutual uncertainties. We suppose that our results for the density are more accurate than the available experimental data in this region of the phase diagram.