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Description
Macroscopic conservation laws fundamentally bottleneck the time evolution of isolated quantum many-body states. We demonstrate that time-evolved states in ergodic disordered models act as typical states drawn from an instantaneous Scrooge ensemble $\rho(t)$—an ensemble that maximizes randomness subject to restriction on local charge profiles. Analytical predictions from this framework excellently match exact unitary evolution, revealing that the complex growth of entanglement and participation entropies is fundamentally restricted by underlying hydrodynamics. Furthermore, extending this approach to integrable systems reproduces the results of generalized hydrodynamics, explicitly recovering the quasiparticle picture formula for entanglement entropy growth following inhomogeneous quantum quenches.