Although the idea of combining thermodynamics with quantum mechanics is more than a century old, quantum thermodynamics has seen significant development over the past few decades. Understanding work, heat, and entropy in the quantum regime has become increasingly important, particularly in light of advances in quantum technologies. This thesis investigates work processes in quantum spin chains. Quantum work processes can involve genuinely quantum features such as entanglement, coherence, and measurement back-action, which are absent in classical thermodynamic descriptions, making their characterization an area of ongoing interest in quantum thermodynamics. Focusing first on a single work step, we show that the frictional work due to finite-time driving for a non-integrable quantum spin chain can be well quantified by the diagonal entropy production. We further demonstrate that integrability breaking enhances work extraction in the adiabatic limit, while suppressing it in the non-adiabatic regime. We then study a quantum Otto cycle using the transverse-field Ising model as the working substance. We determine how different types of operation (engine, refrigerator, accelerator, heater) can emerge for different parameter regimes. We show that with infinitesimal work strokes, a thermal machine behaves either as an engine or an accelerator, and that these regimes can be characterized by equilibrium transverse magnetization. At low temperatures, these regimes are governed by low-energy excitations, while at high temperatures they follow from a free-energy expansion in inverse temperature. Frictional effects can emerge and suppress the engine performance during non-adiabatic driving. We show that these effects can be mitigated using an optimised drive protocol based on a geometric formulation of the path of the system through parameter space. Overall, this thesis provides a comprehensive understanding of how integrability, coherence, finite-time driving, and non-adiabatic transitions govern work extraction and thermal machine operation in quantum spin chains, and paves the way for understanding these processes in other quantum many-body systems.
Although the idea of combining thermodynamics with quantum mechanics is more than a century old, quantum thermodynamics has seen significant development over the past few decades. Understanding work, heat, and entropy in the quantum regime has become increasingly important, particularly in light of advances in quantum technologies. This thesis investigates work processes in quantum spin chains. Quantum work processes can involve genuinely quantum features such as entanglement, coherence, and measurement back-action, which are absent in classical thermodynamic descriptions, making their characterization an area of ongoing interest in quantum thermodynamics. Focusing first on a single work step, we show that the frictional work due to finite-time driving for a non-integrable quantum spin chain can be well quantified by the diagonal entropy production. We further demonstrate that integrability breaking enhances work extraction in the adiabatic limit, while suppressing it in the non-adiabatic regime. We then study a quantum Otto cycle using the transverse-field Ising model as the working substance. We determine how different types of operation (engine, refrigerator, accelerator, heater) can emerge for different parameter regimes. We show that with infinitesimal work strokes, a thermal machine behaves either as an engine or an accelerator, and that these regimes can be characterized by equilibrium transverse magnetization. At low temperatures, these regimes are governed by low-energy excitations, while at high temperatures they follow from a free-energy expansion in inverse temperature. Frictional effects can emerge and suppress the engine performance during non-adiabatic driving. We show that these effects can be mitigated using an optimised drive protocol based on a geometric formulation of the path of the system through parameter space. Overall, this thesis provides a comprehensive understanding of how integrability, coherence, finite-time driving, and non-adiabatic transitions govern work extraction and thermal machine operation in quantum spin chains, and paves the way for understanding these processes in other quantum many-body systems.
We identify and interpret the possible quantum thermal machine regimes with a transverse-field Ising model as the working substance. In general, understanding the emergence of such regimes in a many-body quantum system is challenging due to the dependence on the many energy levels in the system. By considering infinitesimal work strokes, we can understand the operation from equilibrium properties of the system. We find that infinitesimal work strokes enable both heat engine and accelerator operation, with the output and boundaries of operation described by macroscopic properties of the system, in particular the net transverse magnetization. At low temperatures, the regimes of operation and performance can be understood from quasiparticles in the system, while at high temperatures an expansion of the free energy in powers of inverse temperature describes the operation. The understanding generalises to larger work strokes when the temperature difference between the hot and cold reservoirs is large. For hot and cold reservoirs close in temperature, a sufficiently large work stroke can enable refrigerator and heater regimes. Our results and method of analysis will prove useful in understanding the possible regimes of operation of quantum many-body thermal machines more generally.
The maximum work extractable from a quantum system is achieved when the system is driven adiabatically. Frictional work ⟨W⟩fric then quantifies the difference in work output between adiabatic and non-adiabatic driving. Here we show that frictional work in a non-integrable spin chain is well-characterized by the diagonal entropy production ΔSd associated with the build up of quantum coherence. We show that, over a broad range of parameters, ⟨W⟩fric≈TτΔSd, with Tτ the effective temperature of the final time-evolved state. The relationship breaks down for fast protocols at low temperatures, in which case frictional work is instead well-described by the quantum relative entropy between the time-evolved state and a Gibbs-state approximation of the adiabatic state. We compare our results to those obtained from an integrable spin chain, in which case the system is no longer described by a single temperature. In this case, the frictional work is described by a sum of terms for each independent subspace of the spin chain, which are at different effective temperatures. Finally, we show how integrability breaking can enhance work extraction in the adiabatic limit, but degrade work extraction in sufficiently non-adiabatic regimes.
The development of the theory of thermodynamics dates back nearly two centuries, to when the need arose to comprehend and enhance the performance of a novel technology of that era, the heat engine. Extending the classical concepts related to the properties of heat and work into the quantum realm forms the foundation of an emerging field of research known as quantum thermodynamics. To unify the disparate theories of classical thermodynamics and quantum mechanics, a thoroughly developed theoretical framework is necessary. Quantum heat engines provide a fundamental platform for this purpose. Many-body quantum heat engines, in particular, can provide important insights into the potential utilisation of exotic quantum phenomena, such as entanglement and quantum coherence, for building quantum devices that can surpass their classical counterparts in performance. One-dimensional (1D) Bose gases are a paradigmatic example of an interacting quantum many-body system that can be used as a versatile platform for building heat engines to test the thermodynamic theories in the quantum regime. The versatility of this platform comes through the routine experimental realisability of 1D Bose gases, with precise control of their internal and external properties, such as the strength of inter-atomic interactions and external confinement, and the presence of quantum many-body effects. In recent years, there has been an increased focus on exploiting the unique properties of ultracold atomic gases to realize many-body quantum heat engines. Despite this heightened attention and the resulting significant advances at the level of theoretical proposals, experimental feasibility and practical utilization of such engines remains at its infancy. Achieving significant advances at the experimental level requires a deeper understanding of the fundamental components of quantum-gas heat engines. Motivated by this goal, in this thesis we propose a novel and experimentally realistic quantum many-body heat engine that operates in an Otto cycle and uses a weakly interacting harmonically trapped 1D Bose gas as a working fluid. To execute work during the work strokes, we use a quench of the strength of interparticle interactions; when the quench is sudden with respect to the longitudinal dynamics, it maximises the power output. The interaction-induced work strokes are implemented by treating the working fluid as an isolated quantum many-body system undergoing a dynamical evolution starting from a finite temperature thermal equilibrium state. Furthermore, to optimize the performance of this interaction-driven quantum Otto cycle in an experimental scenario, we undertake a comprehensive numerical investigation of the dynamics of the system-reservoir coupling during the heat transfer strokes. We model the heat transfer strokes by treating the working substance as an open quantum many-body system that is coupled to a reservoir.After providing an overview of recent advances in the field of quantum thermodynamics and the background theory of 1D Bose gases in Chapters 1 and 2 we present the main results of this thesis in Chapters 3, 4 and 5. In Chapter 3, we study the individual interaction-induced work strokes of the Otto cycle with a weakly interacting 1D Bose gas as the working fluid. We evaluate the instantaneity of the sudden quench, specifically, identifying the minimum timescales required to perform the sudden quench of the interaction strength without invoking the transverse dynamics. Knowledge of these timescales enables us to perform the sudden quench in an experimental setting while ensuring that the system retains its 1D characteristics and the theory of 1D Bose gas is applicable. Additionally, we determine the time scales governing the opposite scenario of near-adiabatic quench which corresponds to minimum irreversible work in the engine cycle and hence maximum efficiency. This will help us benchmark the sudden quench engine's performance compared to a nearly ideal (near-adiabatic) scenario corresponding to maximum efficiency.Next, in Chapter 4, we analyze the heat transfer strokes of the Otto cycle, where the system is coupled to a reservoir. Using the c-field approach, we simulate the coupling dynamics of the system with both finite and infinite-size reservoirs. During the heat transfer stroke of the quantum Otto cycle, we treat the working fluid as an open quantum many-body system that is in thermal and diffusive contact with another quantum many-body system serving as the reservoir. In our real-time dynamical simulations of the engine strokes, we use a c-field approach based on the stochastic projected Gross-Pitaevskii equation. This approach enables us to treat both the working fluid and the hot and cold reservoirs as independent quantum many-body systems with chemical potential and temperature imbalances. To model the heat transfer strokes of such an engine with a finite-size reservoir, we use a tunnel-coupled model of two quasicondensates that treats both the system and the reservoir microscopically. Our analysis incorporates the impact of both finite-time operation and finite-size reservoirs in the engine cycle to gain a deeper understanding of the operational feasibility of such engines. Our results indicate that, in contrast to the common assumption of near-instantaneous heat transfer between the system and the reservoir, the thermalisation time of the system during these heat transfer strokes is non-negligible when compared to the duration of work strokes even in the near-adiabatic quench. This observation holds true even in the case of coupling the system with an infinite reservoir during the heat transfer strokes. Moreover, we demonstrate that for a finite-size reservoir, the initial dynamics (namely fast initial energy transfer) in the tunnel-coupled model of two quasicondensates can be leveraged to reduce the total driving time and hence increase the power output of the engine. Finally, in Chapter 5, we explore an alternate protocol that involves performing chemical work on the system during the heat transfer strokes to boost the efficiency and power output of the quantum Otto engines with a 1D Bose gas as a working fluid. We compare the performance of the sudden quench engine with an engine driven by a near-adiabatic and a finite-time quench of the interaction strength with respect to the longitudinal dynamics. We then conclude the thesis by summarising our main findings and presenting open questions for future work in the final chapter, Chapter 6.
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.
We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.
Developments in the thermodynamics of small quantum systems envisage nonclassical thermal machines. In this scenario, energy fluctuations play a relevant role in the description of irreversibility. We experimentally implement a quantum heat engine based on a spin-1/2 system and nuclear magnetic resonance techniques. Irreversibility at a microscope scale is fully characterized by the assessment of energy fluctuations associated with the work and heat flows. We also investigate the efficiency lag related to the entropy production at finite time. The implemented heat engine operates in a regime where both thermal and quantum fluctuations (associated with transitions among the instantaneous energy eigenstates) are relevant to its description. Performing a quantum Otto cycle at maximum power, the proof-of-concept quantum heat engine is able to reach an efficiency for work extraction (η≈42%) very close to its thermodynamic limit (η=44%).