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