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We demonstrate the existence of universal features in the finite-timethermodynamics of quantum machines by considering a many-body quantum Ottocycle in which the working medium is driven across quantum critical pointsduring the unitary strokes. Specifically, we consider a quantum engine poweredby dissipative energizing and relaxing baths. We show that under very genericconditions, the output work is governed by the Kibble-Zurek mechanism, i.e., itexhibits a universal power-law scaling with the driving speed through thecritical points. We also optimize the finite-time thermodynamics as a functionof the driving speed. The maximum power and the corresponding efficiency take auniversal form, and are reached for an optimal speed that is governed by thecritical exponents. We exemplify our results by considering a transverse-fieldIsing spin chain as the working medium. For this model, we also show how theefficiency and power vary as the engine becomes critical.

Universal finite-time thermodynamics of many-body quantum machines from Kibble-Zurek scaling