A new perspective to formulate a dissipative thermo field dynamics

•Thermal dissipations are studied from the view point of thermo field dynamics.•Thermal dissipations are renormalized into the non-Hermitian interactions between the original and tilde spaces.•We propose a new perspective of the double Hilbert space on the thermo field dynamics as a heat bath.•The present new perspective is applied to a many-body system in order to clarify thermal fluctuations.•In general, the tilde space does not correspond to the heat bath directly, but corresponds to it through effective non-Hermitian interactions.

In the present study, we propose a new perspective on thermal dissipation based on the thermo field dynamics. From the view point of the renormalization theory, there appear effective interactions between the original and tilde spaces on thermo field dynamics with reducing thermal disturbances. This study yields the equivalence of the following two pictures, namely such a spin system with a random field due to a heat bath as is defined in a Hilbert space and a finite-size system with effective interactions defined in a double Hilbert space. The correspondence of the above two systems yields such perspective that the thermal disturbance is described by the effective non-Hermitian interactions.