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Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations

Controlled Quantum Dynamics Theory Group, Imperial College London, London SW7 2BW, UK
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Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(1), 111; https://doi.org/10.3390/e22010111
Received: 20 December 2019 / Revised: 13 January 2020 / Accepted: 14 January 2020 / Published: 16 January 2020
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.
Keywords: fluctuation relation; Crooks equality; quantum thermodynamics; coherence; athermality; photon added thermal state; photon subtracted thermal state; binomial states; generalised coherent states fluctuation relation; Crooks equality; quantum thermodynamics; coherence; athermality; photon added thermal state; photon subtracted thermal state; binomial states; generalised coherent states
MDPI and ACS Style

Holmes, Z.; Hinds Mingo, E.; Chen, C. .-R.; Mintert, F. Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations. Entropy 2020, 22, 111.

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