## Entropy

The entropy of a discrete probability distribution pr(.) over X is
∑_{x∈X} pr(x) . log(pr(x)).
If the base is two the units are *bits* and
if the base is e the units are *nits*.

The ideal gas is a two-dimensional simulation where momentum and energy are conserved. Calculations are performed using integers so that there are no rounding errors. It illustrates how, at the the level of fundamental particles, with deterministic time-reversible physics, it is not possible to identify "forwards" from "backwards" while watching a movie of the gas which might actually be playing in either direction.