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When a quantum system is placed in thermal environments, we often assume thatthe system relaxes to the Gibbs state in which decoherence takes place in thesystem energy eigenbasis. However, when the coupling between the system and theenvironments is strong, the stationary state is not necessarily the Gibbs statedue to environment-induced decoherence which can be interpreted as continuousmeasurement by the environments. Based on the einselection proposed by Zurek,we postulate that the Gibbs state is projected onto the pointer basis due tothe continuous measurement. We justify the proposition by exact numericalsimulation of a pair of coupled qubits interacting with boson gases.Furthermore, we demonstrate that heat conduction in non-equilibrium steadystates can be suppressed in the strong coupling limit also by theenvironment-induced decoherence.

Steady state thermodynamics of two qubits strongly coupled to bosonic environments