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.
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.
We first derive the Jarzynski relation [1] between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. We then comment on the information-theoretic underpinning of Jarzynski’s reasoning which helps explain why the Jarzynski relation holds identically both quantumly and classically [2]. We then present a scheme to verify the quantum non-equilibrium fluctuation relations as encapsulated by Jarzynski. We show that the characteristic function of the work distribution of a quantum system (which is basically equal to the Wick rotated average exponential of the thermodynamical work) can be extracted from Ramsey interferometry of a single probe qubit (which need not itself be pure, though it must not be fully depolarized) [3,4].We first derive the Jarzynski relation [1] between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. We then comment on the information-theoretic underpinning of Jarzynski’s reasoning which helps explain why the Jarzynski relation holds identically both quantumly and classically [2]. We then present a scheme to verify the quantum non-equilibrium fluctuation relations as encapsulated by Jarzynski. We show that the characteristic function of the work distribution of a quantum system (which is basically equal to the Wick rotated average exponential of the thermodynamical work) can be extracted from Ramsey interferometry of a single probe qubit (which need not itself be pure, though it must not be fully depolarized) [3,4]. An interesting fact is that while the quantum version of the Jarzynski equality remains satisfied even in the presence of quantum correlations, the individual thermodynamical work moments in the expansion of the free energy are, in fact, sensitive to the genuine quantum correlations [5]. Whether this is a fortuitous coincidence remains to be seen, but it certainly goes towards explaining why the laws of thermodynamics happen to be so robust as to be independent of the underlying micro-physics.We intend to elucidate the subtle connection between Jarzynski’s relation and the “quantum arrow of time”. Finally we comment on the fact that our scheme for measuring the quantum work characteristic function belongs to the computational class known as DCQ1 [6], namely all computations that can be performed with only one pure qubit (and N maximally mixed ones).
Quantum thermodynamics seeks to extend the laws of thermodynamics to equilibrium and non-equilibrium systems on the nano-scale. Over the last decade a large body of theoretical research into quantum thermodynamics has been produced; however, experimental research is yet to catch up with the impressive lead set by theory. This is especially true of quantum information theoretic approaches which have proven an effective means of incorporating quantum effects into thermodynamics but seem resistant to experimental implementation. This thesis aims to counter this shortcoming by proposing concrete physical realisations} of quantum thermodynamics to help bridge the gap between theory and experiment. This task is approached directly in chapter 2 by constructing an experimental implementation of a fluctuation relation developed from a quantum information theoretic perspective. Our proposal involves the autonomous evolution of a trapped ion and uses a tapered laser beam to implement a position dependent AC Stark shift. In order to test the fluctuation relation we convert the abstract framework of an autonomous quantum Crooks equality into quantum Crooks equalities for coherent, squeezed and cat states. These new relations highlight the physical origins and implications of coherence induced corrections to classical fluctuation relations and prompt a discussion on the interplay between coherence and irreversibility. In chapter 3 we turn our attention to Gibbs' iconic thought experiments on the work that can be extracted from the mixing of gases. Here we argue that optomechanical setups, involving a cavity in which a membrane is inserted, provide a suitable platform both to generalise such thought experiments to the quantum regime and to explore quantum thermodynamic signatures of distinguishability. We find, in contrast to classical thermodynamics, that the work that can be extracted from the mixing of the two photon gases varies continuously with their distinguishability. Finally, we demonstrate that the bunching of photons, arising from their Bosonic character, generates an energetic footprint that does not exist in classical thermodynamics.
Fluctuation theorems provide universal constraints on nonequilibrium energy and entropy fluctuations, making them a natural framework to assess how and to what extent quantum resources become thermodynamically relevant. We develop a unified framework for incorporating a generic quantum resource, including athermality, quantum coherence, and entanglement, into fluctuation theorems. We work within the end point measurement scheme, which avoids an initial energy measurement and allows quantum resources in the initial state to affect nonequilibrium energy statistics. We derive a family of quantum fluctuation theorems, including generalized Jarzynski equalities and Crooks type fluctuation relations, in which corrections decompose into resource resolved contributions. For single systems, we introduce the concept of weight of athermality, and combine it with the weight of coherence to isolate distinct thermodynamic effects of these quantum resources. For bipartite systems, we furthermore obtain two families of entanglement-resolved fluctuation theorems using an appended correlation operator and the best separable approximation, respectively. Finally, we introduce the concepts of coherence and entanglement fluctuation distances, as Kullback Leibler divergences, which quantify the thermodynamic relevance of quantum resources in a process-dependent and operational manner.
Abstract We investigate manipulations of pure quantum states under incoherent or strictly incoherent operations assisted by a coherence battery, that is, a storage device whose degree of coherence is allowed to fluctuate in the process. This leads to the derivation of fluctuation relations for quantum coherence, analogous to Jarzynski’s and Crooks’ relations for work in thermodynamics. Coherence is thus revealed as another instance of a physical resource, in addition to athermality and entanglement, for which a connection is established between the majorisation framework (regulating pure state transformations under suitable free operations) and the emergence of fluctuation theorems. Our study is hoped to provide further insight into the general structure of battery assisted quantum resource theories, and more specifically into the interplay between quantum coherence and quantum thermodynamics.
There are two related theorems which hold even in far from equilibrium, namely fluctuation theorem and Jarzynski equality. Fluctuation theorem states the existence of symmetry of fluctuation of entropy production, while the Jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes. On the other hand, the relationship between these theorems was investigated by Crooks [Phys. Rev. E 60, 2721 (1999)] for the classical stochastic systems. In this paper, we derive quantum analogues of fluctuation theorem and Jarzynski equality in terms of microscopic reversibility. In other words, the quantum analog of the work by Crooks is presented. Also, for the quasiclassical Langevin system, microscopically reversible condition is confirmed.
Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force.