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.
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.
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
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.
The thermodynamical behavior of quantum systems at the nanoscale is often very difficult to capture via standard frameworks of thermodynamics. The latter is, in fact, an equilibrium theory whose predictions are typically only valid on average, and in regimes where systems are composed of a very large number of constituents. In reality, the thermodynamical behavior of nanoscale systems can be much more constrained that what is predicted by macroscopic thermodynamics, due to the unavoidable impact of fluctuations. As a result, the fundamental limitations to a system's dynamics induced by macroscopic thermodynamics might turn out to be considerably less stringent than what can actually be observed at those scales. The theory of open quantum systems is certainly a powerful tool in this context, and can provide solutions which go beyond equilibrium treatments, but solving the dynamics of an open system requires detailed information about its microscopic structure (e.g. system-environment interactions and coupling strengths). In other words, one of the great advantages of macroscopic thermodynamics, i.e. its universality and independence of microscopic details, might be essentially lost if we can only infer thermodynamical results once we specify the full microscopic structure of our system-environment interaction. This highlights the necessity for a framework of thermodynamics that is well suited for studying the behavior of small quantum systems far from equilibrium, but can still be applied to physical systems in a universal way, i.e., without having to specify full microscopic information. Quantum Resource Theories (QRTs), and in particular the formulations of quantum thermodynamics that have emerged from them, constitute a promising tool in this direction. However, these models of thermodynamics have not yet been extensively applied to realistic physical platform, and their consequences on known thermodynamical processes are still unexplored. Furthermore, going beyond a purely thermodynamical context, a case can be made for the use of general QRTs as benchmarking tools for the certification of certain quantum resources. In other words, QRTs could be used to find fundamental bounds to physical quantities or impossibility results (in the form of no-go theorems) that, when compared to experimental data, can be used to falsify specific hypotheses. In this thesis, both these directions will be explored, by considering resource-theoretical questions that are relevant for different physical platforms. These will include the photochemical process of photoisomerization, heat transport in harmonic systems, and tabletop tests of quantum gravity.
Within quantum information, a very productive way to look at physical phenomena is under the light of the framework of resource theories. Through it, one can focus on questions such as in what sense a particular physical feature can be thought of as a resource for certain tasks, and how can it be quantified. A particularly prominent example of this is the theory of quantum entanglement. In recent years, a research program has emerged in which researchers are trying to build a resource theory relevant for thermodynamical and non-equilibrium phenomena at the quantum and nano scales. The overarching aim is to find how the perspective given by quantum information tools and techniques help us understand new and existing results of the field. In this thesis we advance these efforts by introducing different kinds of non-equilibrium fluctuations into the theory: fluctuations of work and fluctuations of states. In this way, we manage to merge a number of ideas from the field of stochastic thermodynamics into the resource-theoretic framework. We further explore the structure of this resource theory by introducing results in which the finiteness of the heat bath's size is considered, deriving corrections to well-known expressions regarding work extraction. On top of this, we also consider the usefulness within non-equilibrium thermodynamics of other tools coming from quantum information theory, such as the relative entropy and the idea of a recovery map. The connection between the recovery map and the property of quantum detailed balance (and time reversal more generally) is highlighted, and a bound on the entropy production of Davies maps is derived inspired by recent results on quantum information.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.