  We investigate the fundamental dimensional limits to thermodynamic machines.
In particular we show that it is possible to construct self-contained
refrigerators (i.e. not requiring external sources of work) consisting of only
a small number of qubits and/or qutrits. We present three different models,
consisting of two qubits, a qubit and a qutrit with nearest-neighbour
interactions, and a single qutrit respectively. We then investigate fundamental
limits to their performance; in particular we show that it is possible to cool
towards absolute zero.
