Time-reversal symmetry of most conservative forces constrains the properties of linear transport in most physical systems. Here, I study the efficiency of energy transfer in oscillator networks where time-reversal symmetry is broken locally by Lorentz-force-like couplings. Despite their linearity, such networks can exhibit mono-directional transport and allow to isolate energy transfer in subsystems. New mechanisms and general rules for mono-directional transport are discussed. It is shown that the efficiency at maximum power can exceed $1/2$ and may even approach the upper bound of unity.
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