Thermal noise and the emergence of the arrow of time: A simple model

A two-dimensional model of distinguishable particles that obey reversible deterministic laws of motion is used to illustrate the role played by thermal noise in the emergence of irreversible macroscopic behavior. Particles move in an array of square cells with four possible directions of motion. Particles that coincide with one or more particles in the same cell rotate by 90°. We study the evolution of the system from a fine-grained perspective, which allows us to follow the trajectory of each particle, and a coarse-grained perspective. The loss of information due to coarse-graining is compared with the loss of information resulting from noise. It is shown how particle and system trajectories can be used to determine if a system is quasi-ergodic. A modification of the interaction rule ensures that particles undergo momentum-conserving collisions equivalent to those of a simple lattice gas.