Thermodynamic uncertainty relations for three-terminal systems with broken time-reversal symmetry

Abstract: We investigate the thermodynamic uncertainty relations (TURs) in steady-state transport for three-terminal systems within the linear response regime, specifically in the presence of broken time-reversal symmetry. To quantify the TUR, we introduce a dimensionless trade-off parameter $Q_J$, and derive new bounds of $Q_J$ for both particle and heat currents under a strong constraint on the Onsager coefficients. Furthermore, we determine a universal lower bound $Q_J^{bound}\geq1.5$ for three-terminal systems in the linear response regime when the time-reversal symmetry is broken.