Part 6/10:

In 1872, Boltzmann published his crucial Boltzmann equation, which offers a mathematical framework for understanding how probabilities evolve over time within macroscopic systems made up of countless particles. His insights revealed that while atomic motion is reversible on a microscopic scale, the likelihood of returning to an ordered state—such as seeing pieces of glass spontaneously reassemble—is astronomically low. This was a vital perspective that elucidated the apparent contradiction between the reversible equations of motion and the irreversible nature of macroscopic events.