We investigate the relaxation dynamics of open nonintegrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibbs state with a time-dependent effective temperature in the weak-dissipation and thermodynamic limit.
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