  We study an observable-based notion of equilibration and its application to
realistic systems like spin qubits in quantum dots. On the basis of the
so-called distinguishability, we analytically derive general equilibration
bounds, which we relate to the standard deviation of the fluctuations of the
corresponding observable. Subsequently, we apply these ideas to the central
spin model describing the spin physics in quantum dots. We probe our bounds by
analyzing the spin dynamics induced by the hyperfine interaction between the
electron spin and the nuclear spins using exact diagonalization. Interestingly,
even small numbers of nuclear spins as found in carbon or silicon based quantum
dots are sufficient to significantly equilibrate the electron spin.
