Constant-temperature molecular dynamics with momentum conservation

The Nos\'e theorem of the extended-system method of the constant-temperature molecular dynamics is generalized by including the conservation of the total virtual momentum. It is proved that a canonical ensemble of an (N-1)-particle system is generated from an extended system of an N-particle system only if the total virtual momentum is zero. It is also shown that the resulting (N-1)-particle system has a slightly different mass spectrum than that of the original N-particle system. The consequences of this new mass spectrum are relevant in the calculation of dynamical properties and the relaxation times of the system, but irrelevant to thermodynamic averages. For practical considerations, numerical simulations are performed and tested against this theorem. The differences in application of the Nos\'e theorem and the generalized Nos\'e theorem are discussed.