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The $2 \times 2$-matrix structure of Green's functions is a common featurefor the real-time formalisms of quantum field theory under thermal situations,such as the closed time path formalism and Thermo Field Dynamics (TFD). It hasbeen believed to originate from quantum nature. Recently, Galley has proposedthe Hamilton's principle with initial data for nonconservative classicalsystems, doubling each degree of freedom [Phys. Rev. Lett. 110, 174301 (2013)].We show that the Galley's Hamilton formalism can be extended to quantum fieldand that the resulting theory is naturally identical with nonequilibrium TFD.

From Classical Mechanics with Doubled Degrees of Freedom to Quantum Field Theory for Nonconservative System