Abstract Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories . Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.
Abstract Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories . Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family’s structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd’s engine and Landauer’s Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories’ potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.
Thermodynamics has recently been extended to small scales with resource theories that model heat exchanges. Real physical systems exchange diverse quantities: heat, particles, angular momentum, etc. We generalize thermodynamic resource theories to exchanges of observables other than heat, to baths other than heat baths, and to free energies other than the Helmholtz free energy. These generalizations are illustrated with "grand-potential" theories that model movements of heat and particles. Free operations include unitaries that conserve energy and particle number. From this conservation law and from resource-theory principles, the grand-canonical form of the free states is derived. States are shown to form a quasiorder characterized by free operations, d majorization, the hypothesis-testing entropy, and rescaled Lorenz curves. We calculate the work distillable from-and we bound the work cost of creating-a state. These work quantities can differ but converge to the grand potential in the thermodynamic limit. Extending thermodynamic resource theories beyond heat baths, we open diverse realistic systems to modeling with one-shot statistical mechanics. Prospective applications such as electrochemical batteries are hoped to bridge one-shot theory to experiments.
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system's thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity-the inability to extract work from equilibrium states-implies the thermal state's form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation.
Thermodynamics is one of the main pillars of theoretical physics, and it has a special appeal of having wide applicability to a large variety of different physical systems. However, many assumptions in thermodynamics apply only to systems which are bulk material, i.e. consisting a large number of microscopic classical particles. Due to the advancement of designing nanoscale engines, especially in the light of devices that are used today in the processing of quantum information, is thermodynamics still applicable? Can we refine the core principles of thermodynamics to suit such nanoscale quantum systems as well? The central aim of this thesis is to construct a theory of thermodynamics that holds for nanoscale quantum systems, even those as small and simple as a single qubit. We do this by starting out from the core basics of quantum theory: unitary dynamics on closed quantum systems. We adapt a resource theoretic approach inspired by quantum information theory, which defines the quantum states and operations allowed to be used in a thermodynamic evolution. With this framework that naturally adopts the first law as an energy preserving condition, we show the refinement of both the zeroeth and second law of thermodynamics. The zeroeth law explains the physical significance of the Gibbs thermal state. On the other hand, we show that the second law sees refinement in the quantum nanoregime: instead of having the free energy as the sole quantity dictating the possibility of a thermodynamic state transition, we derive a family of generalized free energies that also constitute necessary conditions for a transition to occur. Moreover, these conditions become sufficient for states which are block-diagonal in the energy eigenbasis. In this thesis, we also brought our approach of thermodynamics to the next step: we apply our findings on the second laws, in order to analyze the maximum achievable efficiency for quantum heat engines. In classical thermodynamics, the Carnot efficiency has been long known as the theoretical maximum which does not depend on the specific structure of the thermal baths used, but only on its temperature. With the additional free energies we discover, we show that although quantum heat engines may achieve the Carnot efficiency, such an achievability is no longer independent of the Hamiltonians of the thermal baths. In other words, we find additional restrictions that surface in the study of quantum nanoscale heat engines, which are a direct consequence of the generalized second laws. This has provided us with a deeper understanding into the fundamental limitations of how efficient devices can be made in the realm of microscopic quantum systems.
Quantum thermodynamics is a blossoming research program that uses tools and ideas from quantum information theory to extend the laws of thermodynamics to the domain of systems to which the laws of quantum mechanics apply and the thermodynamic limit does not necessarily apply. The contributions of this program are both foundational, in providing an approach to constructively derive the laws of phenomenological thermodynamics from the postulates of unitary quantum mechanics in a rigorous and bottom-up fashion, but also prac- tical, in providing the theory for an increasing number of experiments that attempt to build thermodynamic machines at scales that were previously inaccessible. One key mathematical tool used in quantum thermodynamics is the framework of resource theories, specifically the resource theory of thermal operations, in which the thermodynamic interaction of a system with a heat bath and various additional components such as work batteries, clocks or catalysts are modeled. In this cumulative thesis, various extensions and modifications of this framework are studied in order to derive novel results and insights about the possible thermodynamic evolution of quantum systems. In particular, following a system- atic exposition of the resource theory of thermal operations from first principles, I develop answers to the following questions: i) What is the smallest heat bath required to provide the necessary randomness for a system to undergo a given stochastic or thermodynamical evolution? ii) Does this size differ depending on whether the interaction between bath and system is quantum or classical? iii) How can quantum systems thermodynamically evolve in the presence of catalytic bystander systems and how can this be put to use? iv) What are the thermodynamic state transitions that an agent can operationally affect when she only has access to partial information about the underlying states of system and bath? v) How can we understand the emergence of the canonical ensemble in statistical thermodynamics from quantum mechanics? These questions cover a wide ground, but it will become clear that they can in fact all be discussed using the same formal tools. As such, the answers to the above questions provided in this thesis are both interesting in their own right — showing for example that there exists a gap in how efficiently randomness can be exploited quantumly as compared to classically or that catalytic bystander systems can be used to extract finite amounts of work per particle from macroscopic systems with non-vanishing probability — as well as illustrate the power of quantum thermodynamics as a set of tools to connect quantum mechanics and the theory of thermodynamics more generally.
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.
We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the informational content of a theory from the concrete details of its formalism. In this framework, we extend the treatment of microcanonical thermodynamics, namely the thermodynamics of systems with a well-defined energy, beyond the known cases of classical and quantum theory, formulating two necessary requirements for a well-defined thermodynamics. We adopt the recent approach of resource theories, where one studies the transitions between states that can be accomplished with a restricted set of physical operations. We formulate three different resource theories, differing in the choice of the restricted set of physical operations. To bridge the gap between the objective dynamics of particles and the subjective world of probabilities, one of the core issues in the foundations of statistical mechanics, we propose four information-theoretic axioms. They are satisfied by quantum theory and more exotic alternatives, including a suitable extension of classical theory where classical systems interact with each other creating entangled states. The axioms identify a class of theories where every mixed state can be modelled as the reduced state of a pure entangled state. In these theories it is possible to introduce well-behaved notions of majorisation, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. The three resource theories define the same notion of resource if and only if, on top of the four axioms, the dynamics of the underlying theory satisfy a condition called "unrestricted reversibility". Under this condition we derive a duality between microcanonical thermodynamics and pure bipartite entanglement.