Thermodynamic bounds on precision in ballistic multi-terminal transport

For classical ballistic transport in a multi-terminal geometry, we derive a universal trade-off relation between total dissipation and the precision, at which particles are extracted from individual reservoirs. Remarkably, this bound becomes significantly weaker in presence of a magnetic field breaking time-reversal symmetry. By working out an explicit model for chiral transport enforced by a strong magnetic field, we show that our bounds are tight. Beyond the classical regime, we find that, in quantum systems far from equilibrium, correlated exchange of particles makes it possible to exponentially reduce the thermodynamic cost of precision.