Bridging the gap between classical and quantum many-body information dynamics

The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens bipartite entanglement entropy, a quantity that describes correlations comprehensive (nonlocal) way. Among most striking features entropy are its unbounded linear growth thermodynamic limit, asymptotic extensivity finite-size systems, and possibility measurement-induced phase transitions, all which have no obvious classical counterpart. Here, we show these key qualitative emerge naturally also spreading, as long one treats problem on par with one, is, by explicitly accounting for exponentially large probability distribution. Our analysis supported extensive numerics prototypical cellular automata Hamiltonian focus mutual introduce ``classical entropy.'' study sheds light nature spreading opens avenues quantum-inspired approaches across physics, theory, statistics.