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Abstract: We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at effective temperature gives a good description of the steady states provided that the system Hamiltonian satisfies the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We numerically show the validity of the perturbation theory in some open quantum systems in spite of the fact that the convergence radius of the perturbation series shrinks to zero in the thermodynamic limit. It is also shown that our theory is not applicable to transport phenomena, in which stationary current of a conserved quantity exists, due to the failure of the perturbation theory. This work suggests a connection between steady states of macroscopic open quantum systems and the ETH.