Hierarchical variational principles of irreversible processes in thermal disturbance

Quantum variational principles of irreversible processes in the linear response theory which have been developed by the present author and his coworker taking the electric conduction as an example are generalized to the transport phenomena in thermal disturbance, where the fluctuation-dissipation law is manifested. By contracting the information, the principle presented at the dynamical stage which concerns no irreversibility is converted into those at the more coarse grained stages, which concerns irreversibility. The conversion takes place from the dynamical to kinetic stage and next from the kinetic to hydrothermodynamical stage.