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The Two Point Measurement scheme for computing the thermodynamic workperformed on a system requires it to be initially in equilibrium. TheMargenau-Hill scheme, among others, extends the previous approach to allow fora non-equilibrium initial state. We establish a quantitative comparison betweenboth schemes in terms of the amount of coherence present in the initial stateof the system, as quantified by the $l_1$-coherence measure. We show that thedifference between the two first moments of work, the variances of work and theaverage entropy production obtained in both schemes can be cast in terms ofsuch initial coherence. Moreover, we prove that the average entropy productioncan take negative values in the Margenau-Hill framework.

Quantum work statistics with initial coherence