Abstract Heat and work in thermodynamics refer to the measurement of changes in energy content of external bodies (baths and agents). We discuss the implications of quantum mechanics on the possibility to measure work in the mesoscopic context. The agent is a quantum entity (say an oscillator) that is used to drive the system. An inherent limitation is related to back-reaction, leading to a classical-like restriction. We find that in order to resolve fingerprints of interference, an additional quantum uncertainty limitation should be taken into account in the design of the agent. This quantum limitation is fundamental, not merely noise-like blurring.
Abstract Heat and work in thermodynamics refer to the measurement of changes in energy content of external bodies (baths and agents). We discuss the implications of quantum mechanics on the possibility to measure work in the mesoscopic context. The agent is a quantum entity (say an oscillator) that is used to drive the system. An inherent limitation is related to back-reaction, leading to a classical-like restriction. We find that in order to resolve fingerprints of interference, an additional quantum uncertainty limitation should be taken into account in the design of the agent. This quantum limitation is fundamental, not merely noise-like blurring.
We consider work fluctuation theorems for isolated driven systems and the possibility to probe them in mesoscopic systems. In this context nonequilibrium fluctuation theorems (NFTs) relate work performed on a system as its Hamiltonian varies with time, to equilibrium data of the initial and final states. In a classical context the system energy can be directly measured, while a quantum implementation requires the incorporation of a work agent. Here, as a work agent we consider a dynamical single-coordinate object, which exchanges energy with the system. The work done on the system is defined as the energy reduction of the work agent, which requires an energy measurement of the agent (only) at the end of the process. To justify the applicability of the NFT we require the agent's trajectory to be weakly affected by the energy exchange with the system. We furthermore argue that the uncertainty in the energy measurements imposes an inherent quantum limitation on the validity of the NFT. We demonstrate our findings for a two-level system, and discuss applications to more complex mesoscopic systems.
We consider a generic quantum many-body system initiated at thermal equilibrium and driven by an external parameter, and discuss the prospect for measuring the work done by the varying parameter on the system. While existing methods are based on a full control of the system's Hamiltonian and are thus limited to few-level quantum systems, measuring work in many-body quantum systems remains challenging. Our approach relies on transforming the external parameter into a dynamical ``work agent", for which we consider an harmonic oscillator in a semiclassical coherent state with a large photon number. We define a work generating function which coincides with the standard two-point measurement protocol for work measurement in the limit of a large photon number. While \emph{in principle} it allows to relate the moments of work ⟨Wn⟩ to observables of the work agent, we focus on the average work, which is obtained from energy conservation by the change of the energy of the agent, which can be measured using photon number detection. We illustrate this concept on a transmon-microcavity system, which displays various quantum coherent effects including Landau-Zener Stükelberg interference and collapse and revival of Rabi oscillations. We discuss how our setup allows to measure work in a variety of quantum many-body systems.
In the last decade, experimentalists have demonstrated their impressive ability to control mechanical modes within mesoscopic objects down to the quantum level: it is now possible to create mechanical Fock states, to entangle mechanical modes from distinct objects, and to store quantum information or transfer it from one quantum bit to another, among the many possibilities found in today's literature. Indeed, mechanics is quantum, very much like spins or electromagnetic degrees of freedom; and all of this is, in particular, referred to as a new engineering resource for quantum technologies. However, there is also much more beyond this utilitarian aspect: invoking the original discussions of Braginsky and Caves, where a quantum oscillator is thought of as a quantum detector for a classical field, namely, a gravitational wave, which is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, let them be known or unknown in nature. This Perspective is about this new potentiality that addresses stochastic thermodynamics, potentially down to its quantum version, the search for a fundamental underlying (random) field postulated in recent theories that can be affiliated to the class of the wave-function collapse models, and more generally open questions of condensed matter like the actual nature of the elusive (and ubiquitous) two-level systems present within all mechanical objects. However, such research turns out to be much more demanding than the use of a few quantum mechanical modes: all the known baths have to be identified, experiments have to be conducted in-equilibrium, and the word “mechanics” needs to be justified by a real ability to move substantially the center-of-mass when a proper drive tone is applied to the system.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations.