Part 8/10:

By extending the analogy to entangled systems, one can see how the state of a single entangled quantum coin differs qualitatively from that of a non-entangled classical coin. The entangled coin, while part of a paired superposition, embodies hidden or inaccessible information on its own, resulting in non-zero von Neumann entropy.

Decoding the Second Law Through Entanglement

The relationship between von Neumann entropy and the Second Law is illuminated through the lens of entanglement. As quantum systems interact with their environments, they become entangled, leading to an exponential growth in complexity and a subsequent obscuring of precise state information—essentially a foundation for classical thermodynamic properties like temperature.