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.
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.
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.
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open-system states, and on a principle of minimal dissipation. This principle leads to a unique prescription for the decomposition of the master equation into a Hamiltonian part representing coherent time evolution and a dissipator part describing dissipation and decoherence. Employing this decomposition we demonstrate how to define work, heat, and entropy production, formulate the first and second laws of thermodynamics, and establish the connection between violations of the second law and quantum non-Markovianity.
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.
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open system states, and on a principle of minimal dissipation. This principle leads to a unique prescription for the decomposition of the master equation into a Hamiltonian part representing coherent time evolution and a dissipator part describing dissipation and decoherence. Employing this decomposition we demonstrate how to define work, heat and entropy production, formulate the first and second law of thermodynamics, and establish the connection between violations of the second law and quantum non-Markovianity.
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 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.