Math Playground
Physics

Entropy

Why broken glass doesn't reassemble — disorder always wins.

Entropy is a measure of disorder. The second law of thermodynamics says total entropy never decreases.

Entropy box — let the gas loose
Left half
100%
90 / 90
Right half
0%
0 / 90
ordered (all on one side)mixed — high entropy
t = 0.0 s

Every molecule started crammed in the left half. Nothing is pushing them right — they just wander there.

Quick check

Why does a dropped egg never spontaneously reassemble, even though no law of motion forbids it?

Boltzmann's entropy

W = number of microscopic states matching the macroscopic one; k ≈ 1.38 × 10⁻²³ J/K. More ways to arrange it → more entropy.

You *can* lower entropy locally — a fridge does it, your body does it — but only by dumping more entropy (waste heat) into the surroundings. The total never goes down.

The arrow of time

Most physics laws look the same run backwards. Entropy is the exception: it (statistically) only increases, which is why we remember the past but not the future, and why coffee cools but never spontaneously reheats. Entropy is time's one-way sign.

Why broken eggs don't reassemble — there are vastly more disordered states than ordered ones.