Using methods of quantum information, it has been rigorously proven that for a typical macroscopic nonequilibrium state |φ₀⟩, the evolving state Ô(t)|φ₀⟩ inevitably approaches equilibrium. This complements the numerical experiment previously conducted on an isolated gas model, which observed an irreversible growth of entanglement entropy as distributed information about the initial nonequilibrium was erased. Thus, the second law of thermodynamics and the ergodic hypothesis of statistical physics gain an explanation from the perspective of quantum information dynamics. The key insight: in typical macroscopic systems, the spreading and erasure of nonequilibrium information are unavoidable processes that give rise to irreversibility and entropy growth.
Drop a sugar cube into water — it will dissolve, and the molecules will evenly spread out. This is the growth of entropy, a measure of disorder. Ludwig Boltzmann thought that probability was to blame: there are more chaotic states. But a new proof shows that the system erases information about order — it forgets that the sugar was a cube. At the quantum level, information doesn't disappear but entangles among particles, becoming completely inaccessible — like a book torn apart and scattered by the wind: all the letters are there, but the meaning cannot be restored. John von Neumann first described quantum entropy, and now it has been rigorously proven that such data dispersal is inevitable for any system with many particles. That's why time flows in one direction: dissolved sugar cannot be reassembled, just as tea will never separate back into its components. The system's 'memory' is erased. This understanding will help create energy-efficient nanodevices. But the main surprise: even theoretically, order cannot be restored — information turns into quantum noise, like a whisper in a raging storm.
🎯 Entropy was once called the 'shadow of energy' because it shows how much energy is irretrievably lost for work.
🎬 In Isaac Asimov's story 'The Last Question,' a supercomputer seeks a way to reverse the growth of entropy in the universe.