Lab 03 — Statistical Mechanics
Entropy & Mixing
Two ideal gases — 2,600 particles of green and gold — sit in a box divided by a wall. After a few seconds the wall drops on its own. The particles do nothing but fly straight and bounce — yet they inevitably mix, and never return to the separated state, even though the reversed motion is perfectly allowed by the laws of physics. The chart tracks the mixing entropy S: divide the box into a 16×10 grid and score how evenly green and gold share each cell. A one-way street toward disorder — the second law is not a force; it is what counting configurations inevitably produces.
The wall drops on its own. From then on it is one-way — watch as long as you like, it never goes back
S fluctuates on its way up and occasionally dips — in small systems entropy can briefly decrease (fluctuation theorem). But the chance of every green particle finding the left half again and every gold the right is about 2⁻²⁶⁰⁰: not once in any number of ages of the universe.