Thermoelectric efficiency of three-terminal quantum thermal machines
  The efficiency of a thermal engine working in linear response regime in a multi-terminals configuration is discussed. For the generic three-terminal case, we provide a general definition of local and non-local transport coefficients: electrical and thermal conductances, and thermoelectric powers. Within the Onsager formalism, we derive analytical expressions for the efficiency at maximum power, which can be written in terms of generalized figures of merit. Also, using two examples, we investigate numerically how a third terminal could improve the performance of a quantum system, and under which conditions non-local thermoelectric effects can be observed. 
Francesco Mazza, Riccardo Bosisio, Giuliano Benenti, Vittorio   Giovannetti, Rosario Fazio and Fabio Taddei
cond-mat.mes-hall quant-ph