  Relaxation modes are the collective modes in which all probability deviations
from equilibrium states decay with the same relaxation rates. In contrast, a
first passage time is the required time for arriving for the first time from
one state to another. In this paper, we discuss how and why the slowest
relaxation rates of relaxation modes are reconstructed from the first passage
times. As an illustrative model, we use a continuous-time Markov state model of
vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all
characteristics of the relaxations in KCl nanoclusters come from the fact that
they are hybrids of two kinetically different regions of the fast surface and
slow bulk diffusions. The origin of the different diffusivities turns out to
come from the heterogeneity of the activation energies on the potential energy
landscapes. We also develop a stationary population method to compute the mean
first passage times as mean times required for pair annihilations of
particle-hole pairs, which enables us to obtain the symmetric results of
relaxation rates under the exchange of the sinks and the sources. With this
symmetric method, we finally show why the slowest relaxation times can be
reconstructed from the mean first passage times.
