Part 5/10:
Before delving into von Neumann entropy, it's essential to revisit classical definitions of entropy. One of the earliest definitions came from Rudolf Clausius, who characterized entropy as a measure of the useful work obtainable from moving heat energy. Ludwig Boltzmann expanded this view by associating entropy with the number of possible configurations of particles that yield a specific set of thermodynamic properties, thus reinforcing the idea that systems naturally evolve towards configurations with higher entropy.