In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based predominantly on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two–stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.
In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based predominantly on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two–stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.
Resource theories are a set of tools, coming from the field of quantum information theory, that find applications in the study of several physical scenarios. These theories describe the physical world from the perspective of an agent, who acts over a system to modify its quantum state, while having at disposal a limited set of operations. A noticeable example of a physical theory which has recently been described with these tools is quantum thermodynamics, consisting in the study of thermodynamic phenomena at the nano-scale. In the standard approach to resource theories, it is usually the case that the constraints over the set of available operations single out a unique resource. In this thesis, we extend the resource theoretic framework to include situations where multiple resources can be identified, and we apply our findings to the study of quantum thermodynamics, to gain a better understanding of quantities like work and heat in the microscopic regime. We introduce a mathematical framework to study resource theories with multiple resources, and we explore under which conditions these multi-resource theories are reversible. Furthermore, we investigate the interconversion of resources, i.e., in which situations it is possible to exchange between two different kinds of resources. We then apply this formalism to quantum thermodynamics, where the two resources under consideration are energy and entropy. This multi-resource theory allows us to explore thermodynamics when the system under examination is closed or coupled with a thermal environment with a finite size. In addition to our work on multi-resource theories, we study the states of equilibrium of closed systems, known as passive states, and analyse under which circumstances it is possible to extract energy from these states. We show that passivity is energetically unstable, and that, even for closed systems, the only stable states are those with a well-defined temperature.
To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muirhead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by single-shot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.
Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilized to describe thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. We apply this resource theory to the case of many noninteracting systems and show that all quantum states are classified by their entropy and average energy, even arbitrarily far away from equilibrium. This implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs, or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for other resource theories.
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.
Thermal engines have been one of the principal topics of thermodynamics ever since its beginning. Today, in the era of the second quantum revolution, although the thermal processes in constant temperatures are relatively well understood in the language of resource theories, a framework to describe thermal engines is still in its infancy. In this work we formalize the resource theory of engines, initially put forward in [Quantum 8, 1222 (2024)], and define such quantities as engine efficiency. Then we turn to a detailed study of thermal engines based on free operations arising from the resource theory of athermality under different restrictions: thermal operation, semilocal thermal operations, and local thermal operation with classical communication. In order to provide analytic lower bounds for thermal engine operation we construct tree states—free states which can be obtained from Gibbs state in simple protocol consisting solely of two-level operations. Furthermore, we derive a full description of the engine based on semilocal thermal operations by describing free states, faithful monotones, and catalytic advantages.
The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.