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.
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.
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.
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.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
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.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature . We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
Quantum information science is at the interface of physics and information theory, with applications including quantum computing and communication. Within this science, a resource theory is a detailed study of a particular class of physical processes, under which the possible state transitions are restricted. Given any initial physical state, the possible final states are also restricted. Initial states with a wealth of possible final states can then be considered more valuable than less versatile initial states, leading to a notion of "resourcefulness" of states. The broad goals of a resource theory include (1) to identify, characterize, and quantify resources; (2) to find an efficient way to determine whether an arbitrary instance of resource conversion is possible; and (3) to relate practical applications to resource conversion. In this thesis, we will take the resource-theoretic approach to understanding thermodynamics. The mathematical methods used in this work will enable us to also develop resource theories for measurement uncertainty and reference frames; in fact, the resource-theoretic treatment of thermodynamics is a combination of these two. Our approach is based on a model called thermal operations, applicable on individual quantum-mechanical systems out of thermal equilibrium. We study this model in detail, resulting in a better understanding of the resource of thermal inequilibrium. In a simplified version of the model where quantum coherence is neglected, we find that the conditions for state transitions are already more complex than the classical second law of thermodynamics. We extend the model to quantum systems controlled by classical circuitry. We also extend it to incorporate quantum coherence in the low-temperature limit. Measurement uncertainty is an important element in quantum mechanics. But its current understanding is through particular measures of uncertainty, such as the variance. We apply the resource theory approach to develop a measure-independent formalism for uncertainty, even in the case where the measurement is on part of a composite system with quantum correlations. Under physical processes restricted by some symmetry (e.g. rotational symmetry), asymmetric states act as resourceful reference frames. In this resource theory, we find the rate at which large quantities of resources can be interconverted through measurements.