In this section, we try to apply the perspectives shown in the previous section to many-body systems. It is important
to estimate how the effective thermal noises {Rj(t)} affect the finite-size subsystem H0. Here, we adopt an approach based
on the cluster mean-field theory [24]. At first, the relevant system is divided into two subsystems, namely the finite-size
subsystem Ω and the infinite-size heat bath Ω′
. These systems interact with each other through the interactions located in
the boundary ∂Ω. Thus the Hamiltonian H is expressed as follows;