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From the perspective of quantum thermodynamics, realisable measurements costwork and result in measurement devices that are not perfectly correlated withthe measured systems. We investigate the consequences for the estimation ofwork in non-equilibrium processes and for the fundamental structure of the workfluctuations when one assumes that the measurements are non-ideal. We show thatobtaining work estimates and their statistical moments at finite work costimplies an imperfection of the estimates themselves: more accurate estimatesincur higher costs. Our results provide a qualitative relation between the costof obtaining information about work and the trustworthiness of thisinformation. Moreover, we show that Jarzynski's equality can be maintainedexactly at the expense of a correction that depends only on the system's energyscale, while the more general fluctuation relation due to Crooks no longerholds when the cost of the work estimation procedure is finite. We show thatprecise links between dissipation and irreversibility can be extended to thenon-ideal situation.

Work estimation and work fluctuations in the presence of non-ideal measurements