The efficiency of a thermal engine working in the linear response regime in a multi-terminal 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. Furthermore, 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. , respectively) flowing from the corresponding reservoirs, which have to fulfill the constraints: J J 0 (energy conservation) , j Δ | | ≪ for j=1,2, and k B is the Boltzmann constant. Under these assumptions the relation between currents and biases can then be expressed through the Onsager matrix L of elements L ij via the identity: J J J J 2 Δ = are the generalized forces, and where J J J W J J J J T T J J ( ) J X J J X J X
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