During the last decades, there have been many theoretical and experimental advances both in the extension of thermodynamics to comprise microscopic systems out-of-equilibrium and in the understanding of quantum mechanics.Along with the state-of-the-art capability of controlling fragile quantum systems in a wide variety of physical platforms, this context has paved the way for the current strategic efforts to develop a thermodynamic theory of quantum systems.In this sense, the research field coined as quantum thermodynamics (QT) already plays a key role in the design and development of future quantum-based technologies.More specifically, QT aims both to apply the usual thermodynamic concepts and notions to describe arbitrary non-equilibrium quantum systems and to understand the emergence of classical thermodynamic behaviour from the underlying fundamentally quantum dynamics.However, despite all current progress, there is still no consolidated formalism for a general thermodynamic description of fully autonomous quantum objects.Besides, the lack of consensus on some central aspects, such as the definitions of quantum counterparts of thermodynamic quantities, is particularly notorious.In this thesis, we focus on the energetic analysis within autonomous quantum systems.To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems.From the Schmidt decomposition approach, we identify effective Hamiltonians as the representative operators for characterizing the local internal energies, whose expectation values satisfy the usual thermodynamic notion of energy additivity.In contrast to the currently used methodologies, such procedure treats the subsystems with equal footing and do not rely on any sort of approximations and additional hypotheses, e.g., semi-classical description, weak-coupling regime, strict energy conservation and Markovian dynamics.In short, our proposal contributes to the development of QT by providing a new formalism that does not suffer from the usual restrictive shortcomings and establishes a new and exact route for defining other general thermodynamic quantities to the quantum regime.
During the last decades, there have been many theoretical and experimental advances both in the extension of thermodynamics to comprise microscopic systems out-of-equilibrium and in the understanding of quantum mechanics.Along with the state-of-the-art capability of controlling fragile quantum systems in a wide variety of physical platforms, this context has paved the way for the current strategic efforts to develop a thermodynamic theory of quantum systems.In this sense, the research field coined as quantum thermodynamics (QT) already plays a key role in the design and development of future quantum-based technologies.More specifically, QT aims both to apply the usual thermodynamic concepts and notions to describe arbitrary non-equilibrium quantum systems and to understand the emergence of classical thermodynamic behaviour from the underlying fundamentally quantum dynamics.However, despite all current progress, there is still no consolidated formalism for a general thermodynamic description of fully autonomous quantum objects.Besides, the lack of consensus on some central aspects, such as the definitions of quantum counterparts of thermodynamic quantities, is particularly notorious.In this thesis, we focus on the energetic analysis within autonomous quantum systems.To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems.From the Schmidt decomposition approach, we identify effective Hamiltonians as the representative operators for characterizing the local internal energies, whose expectation values satisfy the usual thermodynamic notion of energy additivity.In contrast to the currently used methodologies, such procedure treats the subsystems with equal footing and do not rely on any sort of approximations and additional hypotheses, e.g., semi-classical description, weak-coupling regime, strict energy conservation and Markovian dynamics.In short, our proposal contributes to the development of QT by providing a new formalism that does not suffer from the usual restrictive shortcomings and establishes a new and exact route for defining other general thermodynamic quantities to the quantum regime.
During the last decades, there have been many theoretical and experimental advances both in the extension of thermodynamics to comprise microscopic systems out-of-equilibrium and in the understanding of quantum mechanics. Along with the state-of-the-art capability of controlling fragile quantum systems in a wide variety of physical platforms, this context has paved the way for the current strategic efforts to develop a thermodynamic theory of quantum systems. In this sense, the research field coined as quantum thermodynamics (QT) already plays a key role in the design and development of future quantum-based technologies. More specifically, QT aims both to apply the usual thermodynamic concepts and notions to describe arbitrary non-equilibrium quantum systems and to understand the emergence of classical thermodynamic behaviour from the underlying fundamentally quantum dynamics. However, despite all current progress, there is still no consolidated formalism for a general thermodynamic description of fully autonomous quantum objects. Besides, the lack of consensus on some central aspects, such as the definitions of quantum counterparts of thermodynamic quantities, is particularly notorious. In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt decomposition approach, we identify effective Hamiltonians as the representative operators for characterizing the local internal energies, whose expectation values satisfy the usual thermodynamic notion of energy additivity. In contrast to the currently used methodologies, such procedure treats the subsystems with equal footing and do not rely on any sort of approximations and additional hypotheses, e.g., semi-classical description, weak-coupling regime, strict energy conservation and Markovian dynamics. In short, our proposal contributes to the development of QT by providing a new formalism that does not suffer from the usual restrictive shortcomings and establishes a new and exact route for defining other general thermodynamic quantities to the quantum regime.
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.
The quest to develop a general framework for thermodynamics, suitable for the regime of strong coupling and correlations between subsystems of an autonomous quantum "universe," has entailed diverging definitions for basic quantities, including internal energy. While most approaches focus solely on the system of interest, we propose that a universal notion of internal energy should also account for the environment in order to keep consistency with the closed-system energy of the universe. We introduce an abstract framework to describe all effective Hamiltonian-based approaches and address a rigorous definition of energy additivity in this context, in both a weak and a strong form, discussing the underlying subtleties. As an illustration, we study a particular two-qubit universe model, obtaining the exact master equations for both parties and calculating their effective Hamiltonians and internal energies as given by the recently devised minimal dissipation approach. In this case, we show that internal energies are neither additive nor conservative, which leads to unphysical features.
The internal energy of individual subsystems is not well defined in interacting quantum systems, leading to ambiguities in the definition of thermodynamic quantities. Applying the Schmidt basis formalism to general bipartite autonomous quantum systems, we demonstrate that the master equation describing subsystem evolution adheres to the principle of minimal dissipation. This enables to define internal energy of each subsystem in a consistent way. Moreover, by utilizing general aspects of open quantum systems, we show that this master equation is unique. We analyze heat and work for each subsystem as derived from this formalism, providing deeper insights into the thermodynamics of interacting quantum systems.
Thermodynamics is a theory of impressive success and a wide range of applicability. Nevertheless, it took about two hundred years after the basic formulation of phenomenological thermodynamics until Boltzmann and Maxwell gave a foundation in terms statistical mechanics based on classical mechanics. The invention of quantum mechanics has triggered various attempts to establish a theory of quantum thermodynamics, i.e., to explain and derive thermodynamics by quantum mechanics only. Recently, a new approach to this question has been developed by Gemmer et al. focusing on the role of the partitioning of the universe into "system" and "environment" and on how the entanglement between those parts and the properties of typical environments lead to a thermal state in the system for almost any instant in time. Within this approach, the emergence of thermodynamic behavior in subsystems of a wide class of autonomous quantum networks could be established although the state of the total system is a pure. This turns our understanding of the emergence of thermodynamics upside down: No longer the presence of ideal (infinitely large and always in equilibrium) makes the system thermodynamic, but thermodynamic behavior of the system itself induced by an appropriate embedding - which by itself does not need to be thermodynamic in any way - becomes the crucial ingredient. Moreover, it was found that not only macroscopic embeddings but also quantum networks as small as 10 spins may serve already as excellent thermal embeddings. In this context, this thesis approaches a number of questions: First, complementary to the emergence of relaxation (heat), how does mechanical control over a system (work) emerge in autonomous quantum systems? What types of embeddings allow for this control, and is there a lower limit of their size? The answer is discussed by making the connection between work, parametric control of a Hamiltonian, and classical driving with the help of the factorization approximation. Using this link, we propose the local effective measurement basis method to determine heat and work currents in arbitrary bipartite quantum systems, and discuss measures of how to assess the thermodynamic functionality of an arbitrary embedding. We then apply these concepts to a minimal model consisting of only a spin and a quantum harmonic oscillator (spin-oscillator model) to demonstrate that even a single oscillator may act as an ideal work reservoir. A slight variation of the model then illustrates the pros and cons of the proposed measures of thermodynamic functionality. Second, since thermodynamics is first and foremost a theory of processes, which need both, thermal and mechanical control, we ask if autonomous quantum networks can implement thermodynamic cycles. We do so by first reviewing some specialties of quantum thermodynamic processes in general and then presenting the autonomous dynamic three spin machine, an autonomous quantum network implementing a thermodynamic cycle, which is driven by a emergent quantum work reservoir as discussed in the first part. Finally, we discuss quantum thermodynamic pseudomachines, a class of models that exhibit machine-like functionality without use of a thermodynamic cycle. This gives an answer to the question how new forms of control that are only found in quantum systems lead to new thermodynamic functionalities. The presented models can all be understood as thermodynamic laser models. In particular, we discuss the extended dissipative Jaynes-Cummings model and its thermodynamic properties. We resolve a conflict between different interpretations of the model by a careful analysis of the model itself and the thermodynamic concepts used by different authors. It is found that the model is an intricate heat transport model and no machine and that its thermodynamic functionality relies on the transition-selective coupling of heat baths to a few-level quantum system.
Quantum thermodynamics (QT) is an emerging field of research that aims to investigate how the laws of thermodynamics and quantum mechanics merge together in small quantum systems.With advances at the necessary technology to control and measure those small physical systems this field has acquired even more importance, not only in the sense that it can be tested, which is a good thing for basic research, but that new applications could be implemented at these scales, so a better comprehension of the limitations imposed by quantum thermodynamics turns out to be of crucial importance for these goals, which forces theoreticians to produce experimentally relevant versions of these new concepts.Another important aspect present at those systems is that part of them work in a regime where its constituents are described by non-thermal states, and in particular non-thermal steady states, which brings to light a different thermodynamic description, usually called steady-state thermodynamics, therefore one of the goals that we are willing to achieve with this thesis is to give an introduction to QT of systems out-of-equilibrium.One of the related subtopics that physicists deal with in QT and the one that we will be focusing on this work are the use of non-thermal stationary states to build heat engines in the quantum domain, and the analyses of the features that this new regime could possibly allow, like the use of quantum resources as a way to overcome classical limitations imposed on its performance, like to attain efficiencies higher than Carnot's or operate in certain regimes unattainable using only classical resources.Therefore, in order to clarify the underlying physics of those systems in a non-thermal regime, any experimentally well suited content is more than welcome.So keeping that in mind we devised an experimentally relevant thermodynamic cycle for a transmon qubit WS interacting with a non-thermal environment composed by two subsystems, an externally excited cavity and a classical heat bath with temperature T. The WS undergoes a non-conventional cycle (different from Otto, Carnot, etc.) through a succession of non-thermal stationary states obtained by slowly varying its bare frequency and the amplitude of the field applied on the cavity.The efficiency of this engine obtains a maximum value up to 47% in the regime of operation used.We also wanted to look for the role played by the different types of coherences, present at the WS, on the behavior of the engine and its efficiency.By different types of coherence we mean the so called modes of coherence, whose definition is based on how they respond to symmetry transformations.We did that for the trivial case of the qubit, that only contains the modes 1 and -1, and that has shown to be extremely important for the efficiency of the machine.The same procedure was repeated for a 3-level system WS.The modes 1 and -1 was again very important, not only to the absolute value of the engine's efficiency but to the regime of operation of the machine.The additional modes, 2 and -2, had a negative impact on the efficiency, reducing its absolute value.This result appears to show some evidences that quantumness won't necessarily bring improvements to the operation of those machines.