I start by summarizing thermoelectric effects, and how we might be able to use them for refrigeration, perhaps to cool nanoscale systems to previously unreachable temperatures (as low as a few mK). However quantum effects cannot be ignored in such low temperature nanoscale systems. Thus, I develop a quantum theory of thermoelectric effects, which is capable of dealing with the highly non-linear effects necessary for efficient refrigerators.
I apply the theory to refrigeration by point-contacts including certain interaction effects, and predict a discontinuity in the cooling response (called a "fold-catastrophe" in mathematics). I then turn to arbitrary quantum systems, and show that there are certain fundamental bounds on heat-flow, some of which correspond to classical thermodynamic laws, while others are purely quantum.
References:
R.S. Whitney, Preprint arXiv:1208.6130
R.S. Whitney, Preprint arXiv:1211.4737