Maxwell's Refrigerator: An Exactly Solvable Model

We describe a simple and solvable model of a device that -- like the "neat-fingered being" in Maxwell's famous thought experiment -- transfers energy from a cold system to a hot system by rectifying thermal fluctuations. In order to accomplish this task, our device requires a memory register to which it can write information: the increase in the Shannon entropy of the memory compensates the decrease in the thermodynamic entropy arising from the flow of heat against a thermal gradient. We construct the nonequilibrium phase diagram for this device, and find that it can alternatively act as an eraser of information. We discuss our model in the context of the second law of thermodynamics.