# Effect of Emergent Distinguishability of Particles in a non-Equilibrium Chaotic System

# Effect of Emergent Distinguishability of Particles in a non-Equilibrium Chaotic System

We consider the behavior of classical particles which evolution consists of free motion interrupted by binary collisions. The fluid of hard balls and the dilute gas with arbitrary short-range interactions are treated, where the total number of particles is moderate (say, five particles). We assume that the decay of correlations, characteristic for chaotic systems, holds (it can be considered proved for hard balls). We show that the numbers of collisions of a given particle with other particles grow effectively as a biased random walk. This is used to prove that over indefinitely long periods of time each particle has preferences: it systematically collides more with certain particles and less with others. Thus certain particles are effectively attracted and certain others are repelled, making the particles effectively distinguishable. The effect is of statistical origin and it reminds of entropic forces.