Relevance of heat flux to correlation in nonequilibrium steady states

We investigate the relation between heat flux and correlation in nonequilibrium steady states (NESSs), especially considering environmental memory effects. We construct a non-Markovian heat transport model using the repeated interactions scheme. The central system consists of system \mathcalS and two memory qubits, coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of ancilla qubits interacting with the central system. We prove that correlation between the central system and ancillas of the reservoir can witness the steady heat flux in the weak-coupling limit, and this consistency holds for heat flow presenting rectification behavior. This theoretical result can be confirmed numerically if and only if the coupling is weak. Furthermore, the non-Markovianity can impact the monotonicity of steady heat flux in the weak-coupling case, and the maximum value of heat current is at the boundary of Markovian and non-Markovian. Our results can be significant for heat management in hybrid open quantum systems or solid-state thermal circuits.