Numerous pivotal concepts have been introduced to clarify the puzzle of relaxation and/or equilibration in closed quantum systems. All of these concepts rely in some way on specific conditions on Hamiltonians $H$, observables $A$, and initial states $\rho$ or combinations thereof. We numerically demonstrate and analytically argue that there is a multitude of pairs $H,A$ that meet said conditions for equilibration and generate some typical expectation-value dynamics, which means $\langle A\left(t\right)\rangle \propto f\left(t\right)$ approximately holds for the vast majority of all initial states. Remarkably we find that, while restrictions on the $f\left(t\right)$ exist, they do not at all exclude $f\left(t\right)$ that are rather adverse or strange regarding thermal relaxation.

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• Eigenstate thermalization
• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics
• Quantum chaos
• Quantum statistical mechanics
• Quantum thermodynamics
• Thermodynamics