In this thesis, I investigate various aspects of one of the most fundamental questions in thermodynamics: what state transformations can quantum systems undergo while interacting with a thermal bath under specific constraints? These constraints may involve total energy conservation, memory effects, or finite-size considerations. Addressing this question leads to (i) a characterisation of the structure of the thermodynamic arrow of time, (ii) a framework bridging the gap between memoryless and arbitrarily non-Markovian thermodynamic processes, and (iii) a derivation of the famous fluctuation-dissipation relation within a quantum information framework. Finally, the last part of this thesis focuses on studying a ubiquitous phenomenon in science, so-called catalysis. It involves using an auxiliary system (a catalyst) to enable processes that would otherwise be impossible. Over the last two decades, this notion has spread to the field of quantum physics. However, this effect is typically described within a highly abstract framework. Despite its successes, this approach struggles to fully capture the behaviour of physically realisable systems, thereby limiting the applicability of quantum catalysis in practical scenarios. Strikingly, I will demonstrate this effect in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst and allows for the deterministic generation of non-classical light in the cavity, as evidenced by sub-Poissonian statistics or Wigner negativity.
In this thesis, I investigate various aspects of one of the most fundamental questions in thermodynamics: what state transformations can quantum systems undergo while interacting with a thermal bath under specific constraints? These constraints may involve total energy conservation, memory effects, or finite-size considerations. Addressing this question leads to (i) a characterisation of the structure of the thermodynamic arrow of time, (ii) a framework bridging the gap between memoryless and arbitrarily non-Markovian thermodynamic processes, and (iii) a derivation of the famous fluctuation-dissipation relation within a quantum information framework. Finally, the last part of this thesis focuses on studying a ubiquitous phenomenon in science, so-called catalysis. It involves using an auxiliary system (a catalyst) to enable processes that would otherwise be impossible. Over the last two decades, this notion has spread to the field of quantum physics. However, this effect is typically described within a highly abstract framework. Despite its successes, this approach struggles to fully capture the behaviour of physically realisable systems, thereby limiting the applicability of quantum catalysis in practical scenarios. Strikingly, I will demonstrate this effect in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst and allows for the deterministic generation of non-classical light in the cavity, as evidenced by sub-Poissonian statistics or Wigner negativity.
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 emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and thermodynamics, with a particular focus on minimizing entropy production in finite-time processes. By employing tools from quantum information theory and geometric thermodynamics, we tackle the challenge of deriving irreversible thermodynamic behavior from the reversible microscopic framework of quantum mechanics. We begin with a comprehensive review of the laws of thermodynamics, setting the stage for the subsequent analyses. We introduce novel developments in quantum thermodynamics through a generalized framework for geometric thermodynamics, which enables the derivation of finite-time corrections beyond the Markovian regime. Building on this foundation, we extend Landauer's principle by incorporating a finite-time correction that highlights the necessity of strong coupling for optimal information erasure processes. This result underscores the emergence of Planckian time as a fundamental speed limit to thermalization. Additionally, we explore how collective effects can be harnessed to reduce energy dissipation in thermodynamic operations, revealing that classical correlations between systems can significantly mitigate dissipation, though this may pose new questions regarding the third law of thermodynamics. Finally, we optimize thermodynamic processes in mesoscopic systems, including quantum dot engines and information engines. These findings not only enhance our understanding of the fundamental limits of irreversibility but also open new avenues for research. Future works will focus on fully exploiting collective effects, aligning these with the third law of thermodynamics, and understanding the thermodynamic consistency of master equations.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of thermodynamical processes naturally allows for auxiliary systems dubbed 'catalysts', i.e., any physical systems facilitating state transformations while remaining essentially intact in their state, like an auxiliary system, a clock, or an actual catalyst. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating a state transformation process. To incorporate the genuine physical role of a catalyst, we identify very significant restrictions on arbitrary state transformations under dimension or mean energy bounds, using methods of convex relaxations. We discuss the implication of these findings on possible thermodynamic state transformations in the quantum regime.
Catalysis plays a key role in many scientific areas, most notably in chemistry and biology. Here we present a catalytic process in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst, and it allows for the deterministic generation of nonclassical light in the cavity. Considering a cavity prepared in a “classical” coherent state, and choosing appropriately the atomic state and the interaction time, we obtain an evolution with the following properties. First, the state of the cavity has been modified, and it now features nonclassicality, as witnessed by sub-Poissonian statistics or Wigner negativity. Second, the process is catalytic in the sense that the atom is deterministically returned to its initial state exactly, and it can be reused multiple times. What is more, we also show that our findings are robust under dissipation and can be applied to scenarios featuring cavity loss and atomic decay. Finally, we investigate the mechanism of this catalytic process, in particular highlighting the key role of correlations and quantum coherence. Published by the American Physical Society 2024
Quantum thermodynamics seeks to extend the laws of thermodynamics to equilibrium and non-equilibrium systems on the nano-scale. Over the last decade a large body of theoretical research into quantum thermodynamics has been produced; however, experimental research is yet to catch up with the impressive lead set by theory. This is especially true of quantum information theoretic approaches which have proven an effective means of incorporating quantum effects into thermodynamics but seem resistant to experimental implementation. This thesis aims to counter this shortcoming by proposing concrete physical realisations} of quantum thermodynamics to help bridge the gap between theory and experiment. This task is approached directly in chapter 2 by constructing an experimental implementation of a fluctuation relation developed from a quantum information theoretic perspective. Our proposal involves the autonomous evolution of a trapped ion and uses a tapered laser beam to implement a position dependent AC Stark shift. In order to test the fluctuation relation we convert the abstract framework of an autonomous quantum Crooks equality into quantum Crooks equalities for coherent, squeezed and cat states. These new relations highlight the physical origins and implications of coherence induced corrections to classical fluctuation relations and prompt a discussion on the interplay between coherence and irreversibility. In chapter 3 we turn our attention to Gibbs' iconic thought experiments on the work that can be extracted from the mixing of gases. Here we argue that optomechanical setups, involving a cavity in which a membrane is inserted, provide a suitable platform both to generalise such thought experiments to the quantum regime and to explore quantum thermodynamic signatures of distinguishability. We find, in contrast to classical thermodynamics, that the work that can be extracted from the mixing of the two photon gases varies continuously with their distinguishability. Finally, we demonstrate that the bunching of photons, arising from their Bosonic character, generates an energetic footprint that does not exist in classical thermodynamics.