Emergence of statistical behavior in many particle mechanical systems: Boltzmann's ideas on macroscopic irreversibility

Abstract

An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never automatically becomes hot (unless we put that in a microwave for heating or on stove etc) and there are numerous examples. This "one sidedness" of physical processes (like cooling of hot cup) is in apparent contradiction with the time reversibility of the dynamical equations of motion (classical or quantum). The process of automatic heating of a cold cup etc is perfectly possible from the dynamical equations perspective. Ludwig Boltzmann explained this "one sidedness" of physical processes starting from dynamical equations (his H-theorem). A criticism was raised by Boltzmann's contemporaries. The origin of this criticism lies in the very philosophy of "mechanism" that was very prevalent in the 19th century. Everyone wanted to understand physical phenomena through Newtonian mechanics (even J. C. Maxwell devised a mechanical mechanism using gears to explain the electromagnetic field!). The central issue was how can one obtain this "one sidedness" (time irreversiblility) if the underlying dynamical laws are time reversible. Number of articles exist in literature on the issue. But those are mathematically oriented and a simple presentation from practical point of view is seriously lacking. This article is an attempt to de-mystify this "paradox" from simple and practical point of view.