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We obtain the Crooks and the Jarzynski non-equilibrium fluctuation relationsusing a direct quantum-mechanical approach for a finite system that is eitherisolated or coupled not too strongly to a heat bath. These results werehitherto derived mostly in the classical limit. The two main ingredients in thepicture are the time-reversal symmetry and the application of the first law tothe case where an agent performs work on the system. No further assumptionsregarding stochastic or Markovian behavior are necessary, neither a masterequation or a classical phase-space picture are required. The simplicity andthe generality of these non-equilibrium relations are demonstrated, giving verysimple insights into the Physics.

Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality