Disorder is Inevitable: The Secret Lies in Information ✛ ✎

Original: "Thermalization and irreversibility of an isolated quantum system II"
· Xue-Yi Guo
arXiv:2506.01351v5 · 2025-06-02 · arXiv non-exclusive · independent analysis · 1 min
Disorder grows because nature erases information about order.

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.

S_\tau = -\sum_{m=1}^{d_x} p_{m,0} \ln p_{m,0}
Measure of nonequilibrium in the distribution of τ-type particles
S = -\sum_{m=1}^{d_x} \sum_{n=1}^{d_y} p_{m,n,0} \ln p_{m,n,0}
Measure of nonequilibrium of the entire system
Scientists
Ludwig BoltzmannRudolf ClausiusJacob BekensteinStephen HawkingJames Clerk MaxwellEdward Witten
Concepts
second law of thermodynamics thermalization zeroth law of thermodynamics irreversibility thermal equilibrium equipartition theorem thermal state information spread quantum heat transport enthalpy non equilibrium state energy conservation principle of maximum entropy boltzmann entropy energy distribution carnot limit open system entanglement generation information processing eternal inflation