Finite hard-rod systems and their thermodynamic limit: Survey of methods and results

We consider N particles, each of mass m and diameter d, moving on a line and interacting via elastic collisions. The particles are enclosed by a freely movable, massless box of length L. The center of mass is assumed to be at rest. We state results on ergodic properties (equivalence of time and ensemble averages, approach to equilibrium) and outline their proof. We also list exact expressions for some expectation values (pair distribution function, pressure, collision frequency, no-collision probability, velocity autocorrelation function) obtained for fixed parameters N,m,d,L and three kinds of ensembles (smallest stationary, microcanonical, canonical) and discuss their thermodynamic limits. The derivation of these results, based on a generalization of a method already used for small systems (N{≤}3), is illustrated here with specific examples.