Josiah Willard Gibbs described another way in which the entropy of a microscopic system would tend to increase over time. Later writers have called this "Gibbs' H -theorem" as its conclusion resembles that of Boltzmann's. Gibbs himself never called it an H -theorem, and in fact his definition of entropy—and mechanism of increase—are very different from Boltzmann's. This section is included for historical completeness.