In the mid-nineteenth century the second law of thermodynamics was an experimental generalisation: entropy does not decrease in an isolated system, heat flows from hot to cold, processes are irreversible. But *why* this held was unclear — and the mechanical laws governing atoms are symmetric in time; run the film backwards and they still hold.

Ludwig Boltzmann's solution was to give up on individual atoms and look at the ensemble. A gas's observed state (pressure, temperature) can be realised by countless different microscopic arrangements, and entropy measures how many arrangements correspond to that state. The formula is carved on his gravestone: S = k log W. From it the second law emerges not as a necessity but as an overwhelming probability: a system moves toward states realised by more arrangements, because such states are incomparably more numerous. Ink dispersed in a glass of water reassembling is not forbidden; it merely has a probability requiring waits far longer than the age of the universe.

Boltzmann met strong opposition from those who rejected the reality of atoms; figures such as Ernst Mach and Wilhelm Ostwald held explanations resting on unobservable entities to be unscientific. Boltzmann took his own life in 1906, probably under severe depression. Three years earlier Einstein's paper on Brownian motion (1905), followed by Perrin's experiments, had put the existence of atoms beyond argument. Statistical mechanics today runs from solid-state physics to black hole thermodynamics and information theory; Shannon's information entropy carries the same mathematical form.