Effect 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. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown previously that due to the ergodicity these numbers grow with time as a biased random walk. We show that this implies that for a typical trajectory in the phase space each particle has "preferences" that are stable during indefinitely long periods of time. During these periods the particle collides more with certain particles and less with others. Thus there is a clearly distinguishable pattern of collisions of the particle with other particles, as determined by its initial position and velocity. The effect holds also for the dilute gas with arbitrary short-range interactions allowing for experimental testing. It is the mechanical counterpart to the classical probabilistic observation that "in a population of normal coins the majority is necessarily maladjusted" \cite{Feller}.