Birthday of Boltzmann (1844) — S = k log W

Ludwig Boltzmann was born in Vienna on February 20, 1844. He spent his career proving that the thermodynamic properties of gases — temperature, pressure, entropy — are not fundamental laws but statistical averages over the behaviour of trillions of molecules. His great formula, S = k log W, engraved on his tombstone in Vienna, says that entropy S is proportional to the logarithm of W, the number of microscopic arrangements corresponding to a macroscopic state. A gas spreads to fill a room because there are vastly more arrangements with the gas spread out than concentrated — not because of any force pushing it. Disorder is not inevitable; it is just overwhelmingly probable.