Numerical investigations of a simple model of a one-dimensional fluid

Various properties of a one-dimensional fluid with nearest neighbor interactions have been studied with the help of a high-speed computer. Because of the simplicity of the interaction potential employed, it is possible to follow the dynamical evolution of the system and so compute meaningful time averages. At the same time, one can compute the values of the corresponding phase averages and so compare the two results. In computing the phase averages t was necessary to use the Lebowitz-Percus method for relating phase averages calculated with one type of ensemble to those calculated with some other type. This necessity arises because one can compute phase averages for an isobaric canonical ensemble in closed form with the type of forces involved, while one needs phase averages for a microcanonical ensemble in order to compare with the time averages. The results of our investigation very clearly showed the necessity of using the latter ensemble in making this comparison. In one case, using a thousand particle system we found the time average of β = 1 /kT to be 4.8353. Its value for an isobariccanonical ensemble was 4.8261 while for a microcanonical ensemble it was 4.8343. In addition to the above equilibrium studies, we have considered the approach to equilibrium of our system starting from a manifestly nonequilibrium state.