EQUIPARTITION AND ERGODICITY IN CLOSED ONE-DIMENSIONAL SYSTEMS OF HARD-SPHERES WITH DIFFERENT MASSES

We show by computer simulation that a one-dimensional closed system of hard spheres with different masses exhibits equipartition. This is true even when the system contains as few as two particles or is nonergodic. Use of periodic boundary conditions gives very different results from the fixed boundaries. For more than two particles, it is shown that, for most mass ratios, the probability of an exact return to the initial state is vanishingly small. The density of states in momentum space accessible by a particular particle corresponds to a uniform density of states in the region allowed by conservation laws. There are special mass ratios for which ergodicity fails and recurrence occurs. Even for these nonergodic cases, equipartition is obtained. The free volume available to each particle is independent of its mass. These results are in contrast with numerous studies of systems using soft, anharmonic interactions and have implications regarding equipartition in molecular-dynamic simulations.