An Effective Hamiltonian in Nonequilibrium Thermo Field Dynamics with a Reservoir

General properties of an effective Hamiltonian in thermo field dynamics, which includes reservoir effects through coarse graining, are investigated. The necessary and sufficient conditions for the effective Hamiltonian to describe the reservoir effect are obtained. The final canonical distribution is discussed with relation to each given interaction. The result gives a quick and easy guide to construct an effective Hamiltonian and to identify the final equilibrium state.