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In recent years a quantum information theoretic framework has emerged forincorporating non-classical phenomena into fluctuation relations. Here weelucidate this framework by exploring deviations from classical fluctuationrelations resulting from the athermality of the initial thermal system andquantum coherence of the system's energy supply. In particular we developCrooks-like equalities for an oscillator system which is prepared either inphoton added or photon subtracted thermal states and derive a Jarzynski-likeequality for average work extraction. We use these equalities to discuss theextent to which adding or subtracting a photon increases the informationalcontent of a state thereby amplifying the suppression of free energy increasingprocess. We go on to derive a Crooks-like equality for an energy supply that isprepared in a pure binomial state, leading to a non-trivial contribution fromenergy and coherence on the resultant irreversibility. We show how the binomialstate equality fits in relation to a previously derived coherent state equalityand offers a richer feature-set.

Quantifying athermality and quantum induced deviations from classical fluctuation relations