Emergence of distinguishability of patterns of collisions of particles in a non-equilibrium chaotic system

We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. This is characterized by counting how many times different pairs collided at a given time. It was shown using plausible assumption of decay of correlations that on coarse-grained time-scale the determination of the particle with which the given particle collides next is like tossing a coin. We demonstrate that this implies that for a typical trajectory in the phase space each particle has stable “preferences” during indefinitely long periods of time whose average is infinite. During these periods the particle persistently collides more with certain particles and less with others. This effect generalizes and can be tested on small gaseous systems with arbitrary short-range interactions.