Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations

Abstract

In recent years a quantum information theoretic framework has emerged for incorporating nonclassical 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.

Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

“…From Remark 19 it follows that ρ and {A (i) j } j=0,1 , i∈{1,...,N −1} must be equal to (up to local isometries) the state and observables of Eq. ( 46), (44), and (45), which proves our claim.…”

“…Then, these are equal to (up to local isometries) the state and observables of Eqs. (46), (44), and (45).…”

“…From this, one can directly determine the relative value of any pair of resources: if resource R can be converted to resource S, then R is at least as valuable as S, since (in the context of these free operations) R can clearly be used for any purpose that S can be used for. There are by now many useful resource theories, including those for LOCC-entanglement [30][31][32], for nonclassicality in Bell scenarios, including LOSR-entanglement [18,33] and other common-cause processes [17,19,20], for post-quantumness [34][35][36], for coherence [37][38][39], for athermality [40][41][42][43][44][45], and so on.…”

Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

“…From this, one can directly determine the relative value of any pair of resources: if resource R can be converted to resource S, then R is at least as valuable as S, since (in the context of these free operations) R can clearly be used for any purpose that S can be used for. There are by now many useful resource theories, including those for entanglement (relative to local operations and classical communication [32][33][34] or relative to local operations and shared randomness [21,35]), for nonclassicality in Bell scenarios [20] and other common-cause processes [22,23], for post-quantumness [36][37][38], for coherence [39][40][41], for athermality [42][43][44][45][46][47], and so on.…”