entropy of the universe
Whenever you study a change, you can split the world into two pieces: the system you care about, and everything else touching it — the 'surroundings.' Add those two entropies together and you have the entropy of the universe, the grand total. It is the one number the second law actually cares about.
The rule is stark. For any real process, the entropy of the universe (system plus surroundings) goes up. For an idealized reversible process, it stays exactly constant. It can never go down. So the system's own entropy is allowed to fall — water can freeze, a cell can organize itself — provided the surroundings' entropy rises by even more to keep the total climbing.
Why it matters: this is the cleanest, most honest form of the second law, and the true test of spontaneity. A reaction proceeds if and only if it increases the universe's entropy; the familiar Gibbs free energy is just a convenient way to track that same total from inside the system at constant temperature and pressure. The humbling caveat: taken to its end, this principle suggests the universe drifts toward an even, lukewarm sameness — the so-called 'heat death' — though over timescales beyond all imagining, and with cosmology adding wrinkles physicists still debate.
When water freezes below 0 °C, the ice is more orderly than the liquid, so the system's entropy drops. Yet freezing releases heat into the cold surroundings, and at that low temperature that heat raises the surroundings' entropy by even more. The universe's total still climbs — which is exactly why the freezing is spontaneous there.
System entropy may fall; the universe's total never does.
'Universe' here is a technical term meaning just the system plus its immediate surroundings — the box and everything it exchanges heat or matter with — not literally the whole cosmos. It is the smallest isolated system that fully contains the process.