Molecular dynamics ensemble, equation of state, and ergodicity - art. no. 011106

The variant of the NVE ensemble known as the molecular dynamics ensemble wa s recently redefined by Ray and Zhang [Phys. Rev. E 59, 4781 (1999)] to inc lude the specification of a time invariant G (a function of phase and, expl icitly, the time) in addition to the total linear momentum M. We reformulat e this ensemble slightly as the NVEMR ensemble, in which RIN is the center- of-mass position, and consider the equation of state of the hard-sphere sys tem in this ensemble through both the virial function and the Boltzmann ent ropy. We test the quasiergodic hypothesis by a comparison of old molecular dynamics and Monte Carlo results for the compressibility factor of the 12-p article, hard-disk systems. The virial approach, which had previously been found to support the hypothesis in the NVEM ensemble, remains unchanged in the NVEMR ensemble. The entropy S approach depends on whether S is defined through the phase integral over the energy sphere or the energy shell, the parameter theta being 0 or 1, respectively. The ergodic hypothesis is found to be supported for theta = 0 but not for theta = 1.