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Producing a large current typically requires large dissipation, as is thecase in electric conduction, where Joule heating is proportional to the squareof the current. Stochastic thermodynamics offers a framework to studynonequilibrium thermodynamics of small fluctuating systems, and quite recently,microscopic derivations and universal understanding of the trade-off relationbetween the current and dissipation have been put forward. Here we establish auniversal framework clarifying how quantum coherence affects the trade-offbetween the current and dissipation: a proper use of coherence enhances theheat current without increasing dissipation, i.e. coherence can reducefriction. If the amount of coherence is large enough, this friction becomesvirtually zero, realizing a superconducting-like ``dissipation-less'' heatcurrent. Since our framework clarifies a general relation among coherence,energy flow, and dissipation, it can be applied to many branches of science. Asan application to energy science, we construct a quantum heat engine cycle thatexceeds the power-efficiency bound on classical engines, and effectivelyattains the Carnot efficiency with finite power in fast cycles. We discussimportant implications of our findings with regard to the field of quantuminformation theory, condensed matter physics and biology.

Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence