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

TL;DR

This paper establishes universal bounds on Onsager coefficients and efficiency for multi-terminal thermoelectric devices in magnetic fields, revealing fundamental limits influenced by the number of terminals and symmetry breaking.

Contribution

It introduces a universal bound on Onsager coefficients in multi-terminal thermoelectric systems with magnetic fields, extending understanding of efficiency limits in such devices.

Findings

Derived a bound on Onsager coefficients depending on terminal count

Bounded efficiency and power for heat engines and refrigerators

Results are independent of the number of terminals in certain cases

Abstract

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.