Multi-terminal Thermoelectric Transport in a Magnetic Field: Bounds on Onsager Coefficients and Efficiency

Thermoelectric transport involving an arbitrary number of terminals is discussed in the presence of a magnetic field breaking time-reversal symmetry within the linear response regime using the Landauer-B\"uttiker formalism. We derive a universal bound on the Onsager coefficients that depends only on the number of terminals. This bound implies bounds on the efficiency and on efficiency at maximum power for heat engines and refrigerators. For isothermal engines pumping particles and for absorption refrigerators these bounds become independent even of the number of terminals. On a technical level, these results follow from an original algebraic analysis of the asymmetry index of doubly substochastic matrices and their Schur complements.