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We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian.
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The continuous-spectrum Hamiltonian was chosen for convenience. It has been shown in [ 3 , 4 ] that discrete weights also work arbitrarily well
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In fact, the expected value of any function of H e H_{e} is conserved
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