Isothermal molecular-dynamics ensembles

S. Nos\'e [Mol. Phys. 52, 255 (1984); J. Chem. Phys. 81, 511 (1984)] has developed a form of molecular dynamics that generates the canonical ensemble. Since molecular-dynamics calculations are carried out at constant total linear momentum, we investigate the necessary modifications in Nos\'e's theory when the constraint of constant total linear momentum is imposed. We show that Nos\'e's theory can be modified so that it generates phase-space trajectories corresponding to a constant-momentum canonical ensemble with zero total momentum. We also present an exact treatment of the statistical mechanics of this constant-momentum canonical ensemble, including expressions relating averages to thermodynamic variables and formulas involving thermodynamic response functions which are often used in molecular-dynamics calculations.