Boltzmann’s quantity H is in fact the entropy of an individual atom, multiplied by minus one. He showed that when the positions and velocities of the atoms are uncorrelated—that is, independent of each other—collisions between them will decrease H and increase the entropy of the individual atoms. Subsequent collisions, he argued, would continue to increase that entropy. He concluded that his H-theorem justified the second law of thermodynamics by supplying a mathematical proof that entropy must increase.
