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We investigate quench dynamics in a one-dimensional spin model, comparingboth quantum and classical descriptions. Our primary focus is on the differenttimescales involved in the evolution of the observables as they approachstatistical relaxation. Numerical simulations, supported by semi-analyticalanalysis, reveal that the relaxation of single-particle energies (globalquantity) and on-site magnetization (local observable) occurs on a timescaleindependent of the system size $L$. This relaxation process is equallywell-described by classical equations of motion and quantum solutions,demonstrating excellent quantum-classical correspondence, provided the systembe strongly chaotic. The correspondence persists even for small quantum spinvalues ($S=1$), where a semi-classical approximation is not applicable.Conversely, for the participation ratio, which characterizes the initial statespread in the many-body Hilbert space and which lacks a classical analogue, therelaxation timescale is system-size dependent.

Timescales of quantum and classical chaotic spin models evolving toward equilibrium