  Environmental noises cause the relaxation of quantum systems and decrease the
precision of operations. Apprehending the relaxation mechanism via
environmental noises is essential for building quantum technologies.
Relaxations can be considered a process of information dissipation from the
system into an environment with infinite degrees of freedom (DoF). According to
this idea, a model of artificial relaxation has been proposed and demonstrated
in NMR experiments. Although this model successfully understood the central
idea of relaxation, we observed recursive behavior, which is non-ideal to
describe relaxation, because of few DoF of the ``artificial environment''. In
this paper, we extend the approach of the artificial environment and discuss,
theoretically and experimentally, how many DoF of the environment are necessary
for realizing ideal relaxation behavior. Our approach will help us thoroughly
understand the concept of relaxation.
