Verification of the quantum nonequilibrium work relation in the presence of decoherence

Although nonequilibrium work and fluctuation relations have been studied in detail within classical statistical physics, extending these results to open quantum systems has proven to be conceptually difficult. For systems that undergo decoherence but not dissipation, we argue that it is natural to define quantum work exactly as for isolated quantum systems, using the two-point measurement protocol. Complementing previous theoretical analysis using quantum channels, we show that the nonequilibrium work relation remains valid in this situation, and we test this assertion experimentally using a system engineered from a trapped ion, adding external noise to produce the effects of decoherence. Our experimental results reveal the work relation's validity over a variety of driving speeds, decoherence rates, and effective temperatures and represent the first confirmation of the work relation for evolution described by a non-unitary master equation.