  The performance characteristics of a heat rectifier and a heat pump are
studied in a non Markovian framework. The device is constructed from a molecule
connected to a hot and cold reservoir. The heat baths are modelled using the
stochastic surrogate Hamiltonian method. The molecule is modelled by an
asymmetric double-well potential. Each well is semi-locally connected to a heat
bath composed of spins. The dynamics is driven by a combined system-bath
Hamiltonian. The temperature of the baths is regulated by a secondary spin bath
composed of identical spins in thermal equilibrium. A random swap operation
exchange spins between the primary and secondary baths. The combined system is
studied in various system-bath coupling strengths. In all cases the average
heat current always flows from the hot towards the cold bath in accordance to
the second law of thermodynamics. The asymmetry of the double well generates a
rectifying effect meaning that when the left and right baths are exchanged the
heat current follows the hot to cold direction. The heat current is larger when
the high frequency is coupled to the hot bath. Adding an external driving field
can reverse the transport direction. Such a refrigeration effect is modelled by
a periodic driving field in resonance with the frequency difference of the two
potential wells. A minimal driving amplitude is required to overcome the heat
leak effect. In the strong driving regime the cooling power is non-monotonic
with the system-bath coupling.
