The Role of Walls' Stochastic Forces in Statistical Mechanics -- Irreversibility and Transition from One Microstate to Large Number of Microstates

A statistical system, by definition, experiences uncontrollable stochastic interactions with the surrounding and allow for irreversibility.$^{(1)}$ A purely deterministic system will not show any irreversibility.$^{(2)}$ One can model the walls of the container containing a system to be the source of these stochastic impulses. We present the results of such stochastic walls' impulses on a single particle in a one-dimensional box of a fixed length. At each collision with the walls, the velocity changes due to stochastic impulses so that the velocity becomes unpredictable. After a long period of time, a single initial velocity results in a distribution of velocities. If the strength of the impulse is not too strong, the average kinetic energy reaches a finite limit, so that it can be used to define the temperature. \\[4pt] 1) ``Irreversibility, molecular Chaos, and A simple proof of the second law'' P.D.Gujrati, http://arxiv.org/abs/0803.1099 (arXiv:0803.1099) \\[0pt] 2) ``Poincare Recurrence, Zermelo's Second Law Paradox, and Probabilistic Origin in Statistical Mechanics'' P.D.Gujrati, http://arxiv.org/abs/0803.0983 (arXiv:0803.0983)