Abstract Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. At the core of this theory is the interconversion between athermality states, i.e. states out of thermal equilibrium. Here, we solve the question of how athermality can be used to heat and cool other quantum systems that are initially at thermal equilibrium. We then show that the convertibility between quasi-classical resources (resources that do not exhibit coherence between different energy eigenstates) is fully characterized by their ability to cool and heat qubits, i.e. by two of the most fundamental thermodynamical tasks on the simplest quantum systems.
Abstract Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. At the core of this theory is the interconversion between athermality states, i.e. states out of thermal equilibrium. Here, we solve the question of how athermality can be used to heat and cool other quantum systems that are initially at thermal equilibrium. We then show that the convertibility between quasi-classical resources (resources that do not exhibit coherence between different energy eigenstates) is fully characterized by their ability to cool and heat qubits, i.e. by two of the most fundamental thermodynamical tasks on the simplest quantum systems.
Chapter 17 delves into quantum thermodynamics, building on the concepts introduced in the resource theory of nonuniformity. This chapter focuses on thermal states and athermality as resources within the quantum domain, emphasizing the significance of Gibbs states and their role in quantum statistical mechanics. It outlines the operational framework for thermal operations, setting the stage for discussions on energy conservation and the second law of thermodynamics in quantum systems. A key aspect of the chapter is the exploration of quasi-classical athermality, illustrating how quantum states deviate from thermal equilibrium when the state of the system commutes with its Hamiltonian. In the fully quantum domain, the chapter introduces closed formulas for quantifying athermality, such as the athermality cost and distillable athermality, both in the single-shot and the asymptotic domains. These measures provide a quantitative understanding of the efficiency of thermal operations and the potential for work extraction or consumption.
Active states, from which work can be extracted by time-dependent perturbations, are an important resource for quantum thermodynamics in the absence of heat baths. Here we characterize this resource, establishing a resource theory that captures the operational scenario where an experimenter manipulates a quantum system by means of energy-preserving operations and resets to non-active states. Our resource theory comes with simple conditions for state convertibility and an experimentally accessible resource quantifier that determines the maximum advantage of active states in the task of producing approximations of the maximally coherent state by means of energy-preserving quantum operations.
Abstract Manipulating thermodynamic resources at the finite-qubit level is a key challenge in quantum thermodynamics. While asymptotic transformations are governed by the relative entropy of athermality, the finite-qubit regime remains unexplored. We systematically investigate the concentration of athermality via thermal operations in the finite-qubit regime. Focusing strictly on diagonal qubit states, where the system’s non-equilibrium character is purely classical, we first establish a necessary and sufficient condition for realizing concentration in the two-qubit scenario, using quantum relative entropy as the resource measure. Leveraging this result, we propose a cascading protocol that achieves the upper bound of athermality amplification at a given temperature. Moreover, we generalize our analysis to Rényi relative entropies to examine how the concentration task depends on the specific measure of athermality. For the three-qubit scenario, we show that concentration can be achieved universally and is independent of the choice of the athermality measures. These results chart the finite-qubit landscape and reveal a sharp dichotomy between two-qubit and three-qubit thermodynamics.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
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.
We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs-preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.