| A statistical system, by definition, experiences uncontrollable stochastic interactions with the surroundings that will give rise to time irreversibility. A purely deterministic (invariant under time reversal) system will not show any irreversibility. One can model the walls of a container containing a system to be the source of these stochastic impulse. We present the results of such stochastic walls' impulses on a single particle in a one dimensional box of a fixed length. The particle moves with a uniform velocity until it hits the wall. At each collision with the wall, the velocity changes due to the stochastic impulse so that velocity becomes unpredictable and hence its effect has to be treated in the probabilistic sense to study the mechanics of the system. A single initial velocity turns into a distribution of velocities after many collisions with the walls. If the strength of the impulse is not too strong, the average kinetic energy reaches to a finite limit and the distribution of velocities follows very closely the Maxwell-Boltzmann distribution as we wait long enough. The temperature of the system at equilibrium can be defined from both the average kinetic energy and the distribution of velocities which agree fairly well with each other. The entropy of the system steadily increases and always reaches to a maximum value suggesting that the system has reached equilibrium. |
