Quantum Relative Entropy of Tagging and Thermodynamics Thermodynamics establishes a relation between the work that can be obtained in a transformation of a physical system and its relative entropy with respect to the equilibrium state. It also describes how the bits of an informational reservoir can be traded for work using Heat Engines. Therefore, an indirect relation between the relative entropy and the informational bits is implied. From a different perspective, we define procedures to store information about the state of a physical system into a sequence of tagging qubits. Our labeling operations provide reversible ways of trading the relative entropy gained from the observation of a physical system for adequately initialized qubits, which are used to hold that information. After taking into account all the qubits involved, we reproduce the relations mentioned above between relative entropies of physical systems and the bits of information reservoirs. Some of them hold only under a restricted class of coding bases. The reason for it is that quantum states do not necessarily commute. However, we prove that it is always possible to find a basis (equivalent to the total angular momentum one) for which Thermodynamics and our labeling system yield the same relation.

Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations 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 systemxe2x80x99s energy supply. In particular, we develop Crookslike equalities for an oscillator system which is prepared either in photon added or photon subtracted thermal states and derive a Jarzynskilike 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 Crookslike equality for an energy supply that is prepared in a pure binomial state, leading to a nontrivial 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 featureset.