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We consider the equilibrium state of a quantum system weakly coupled to a quantum bath within second order perturbation theory. It was previously shown by Romero-Rochin and Oppenheim ͓Physica A 155, 52 ͑1989͔͒ that the equilibrium state deviates from the canonical form, e Ϫ␤H s /Z s (H s is the free system Hamiltonian and Z s the canonical partition function͒. We reproduce this result via a different derivation, starting from the non-Markovian, rather than the Markovian, quantum Masterdoi:10.1063/1.481928 fatcat:nhjsvzqmnjepvdclrsjt3valqa