Why can't some physical processes ever run backward?

Some things only ever happen in one direction: a hot cup of coffee cools down in a cold room, but it never spontaneously heats back up by drawing warmth out of the colder air. The reason comes down to a quantity physicists call entropy, a measure of how spread out and disordered a system's energy is. The second law of thermodynamics says that left alone, the entropy of an isolated system can never decrease, only stay the same or grow, which is exactly why certain processes are irreversible and systems naturally drift toward equilibrium, the state where entropy is as high as it can possibly get.

The idea didn't start out so abstract. In 1803 the French mathematician Lazare Carnot noticed that every machine loses some of its useful motion to jolts and friction, as if nature had a built-in tendency to waste usable energy. His son Sadi Carnot pushed the idea further in 1824, comparing the way heat 'falls' from a hot body to a cold one inside an engine to the way water falls through a water wheel to do work, an early and vivid insight into what would become the second law.

The concept got its name from Rudolf Clausius, who in 1865 gave it a precise mathematical definition, as a tiny amount of heat divided by the temperature at which it flows. He first called it 'transformation-content' in German, then coined a shorter word built from Greek roots for 'transformation': entropy. Fifteen years earlier, in 1850, the engineer William Rankine had already been circling the same idea under less catchy names like 'thermodynamic function.'

It was the Austrian physicist Ludwig Boltzmann who gave entropy its deepest explanation. He showed that entropy simply counts how many different microscopic arrangements of atoms and molecules are consistent with what we observe at the large scale, high entropy meaning there are enormously more disordered arrangements than ordered ones. Boltzmann tied that microscopic picture to the macroscopic world with a simple logarithmic law, introducing the constant that still carries his name today.