The Kac Ring Model
The Kac ring is a simple, explicitly solvable model that illustrates the process of passing from microscopic, time-reversible behavior to macroscopic, thermodynamic behavior . In this model, sites are arranged around a circle, forming a one-dimensional periodic lattice. Each site is occupied by either a black ball or a white ball. A fraction of the bonds joining neighboring sites have a "tunnel." From time to time each ball moves to the clockwise neighboring site, changing its color if the ball crosses a tunnel.
In this model, a "microstate" at time is characterized by quantities: the color (black or white) of balls sitting on each of the sites. A "macrostate" at time is characterized by a single coarse-grained quantity: the difference between the numbers of white and black balls, relative to the total number . The microscopic dynamics are reversible  and recurrent  (the microstate repeats itself after time steps). However, under a molecular chaos assumption (the fraction of white balls just about to cross a tunnel is assumed to be at any time) , the irreversible evolution equation is expected to be correct in the limit .
In this Demonstration, all the balls are white initially. You can control the total number of sites , the fraction of bonds with a tunnel and the time range to display. You can choose to follow the temporal evolution of the macrostate or the microstate.
 G. A. Gottwald and M. Oliver, "Boltzmann's Dilemma: An Introduction to Statistical Mechanics via the Kac Ring," SIAM Review, 51(3), 2009 pp. 613–635. doi:10.1137/070705799.