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 [2] and recurrent [3] (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) [4], 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.