Quantum thermal machines and batteries

Abstract: The seminal work by Sadi Carnot in the early nineteenth century provided the blueprint of a reversible heat engine and the celebrated second law of thermodynamics eventually followed. Almost two centuries later, the quest to formulate a quantum theory of the thermodynamic laws has thus unsurprisingly motivated physicists to visualise what are known as quantum thermal machines' (QTMs). In this article, we review the prominent developments achieved in the theoretical construction as well as understanding of QTMs, beginning from the formulation of their earliest prototypes to recent models. We also present a detailed introduction and highlight recent progress in the rapidly developing field ofquantum batteries'.

• The paper introduces quantum thermal machines and batteries by extending classical thermodynamics to capture quantum energy conversion mechanisms.
• It employs GKSL master equations and cycle analyses, such as Otto and Carnot cycles, to detail non-equilibrium dynamics and efficiency constraints in quantum systems.
• The study highlights the role of quantum coherence, entanglement, and non-thermal reservoirs in enhancing charging speeds and overall performance of quantum batteries.

An Overview of Quantum Thermal Machines and Quantum Batteries

The paper "Quantum thermal machines and batteries" offers a comprehensive overview of the theoretical progress made in the formulation and understanding of quantum thermal machines (QTMs) and quantum batteries. The foundational work underlying classical thermodynamics, such as the Carnot engine and the second law of thermodynamics, is naturally extended into the quantum domain, motivating the exploration of QTMs. Indepth analysis of QTMs contributes to both reconciling macroscopic thermodynamic laws with quantum mechanics and understanding energy conversion and storage at microscopic scales.

Quantum Thermal Machines

Quantum thermal machines have been designed to emulate the function of classical engines but at quantum scales. They consist of quantum systems that interact with thermal reservoirs to convert heat energy into work or vice-versa. Importantly, the dynamical processes in QTMs are often analyzed using the framework of open quantum systems, especially through the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equations. The periodic or continuous modulation of system Hamiltonians introduces non-equilibrium dynamics that are crucial to their operation.

The investigation of QTMs extends to continuous and reciprocating quantum machines. Continuous machines, characterized by their perpetual interaction with heat baths, are particularly practical from an experimental perspective due to reduced requirements for coupling and decoupling processes. Theoretically, these machines are often benchmarked against their classical counterparts, with the efficiency constrained by the Carnot limit being a typical feature, albeit they operate below it due to additional irreversibility in real systems.

Reciprocating quantum machines follow cycles made up of discrete strokes and generally allow clearer theoretical analyses. Quantum analogues of classical cycles such as the Otto, Carnot, and Stirling cycles have been studied extensively. Notably, the quantum Otto cycle remains a focal point due to its simplicity and clear separation of work-performing and heat-exchange processes. Further explorations in this domain have highlighted the impact of non-Markovian dynamics and quantum coherence—effects absent in classical descriptions.

One remarkable area of research within QTMs involves the use of non-thermal baths or reservoirs, such as squeezed thermal baths, to potentially enhance machine performance. These non-classical resources show promise for improving energy conversion efficiencies in specific regimes, albeit conformity with thermodynamic laws remains rigorously intact.

Quantum Batteries

The concept of quantum batteries, which focuses on the storage and efficient utilization of energy at quantum scales, gains significance as it explores the possibility of leveraging quantum phenomena to enhance battery performance. Attention is devoted to the maximal work extraction from quantum states, emphasizing the need to properly define quantum equivalents of 'work' and 'heat.'

The role of passive states is noteworthy in this context, revealing how a quantum system can optimally store energy that is later accessible for useful work upon demand. Collective phenomena, particularly quantum entanglement across multiple battery cells, have been explored to increase charging speeds, termed quantum advantage. Here, quantum speed limits pose significant constraints, instigating an investigation into the feasible bounds of energy deposition and retrieval processes in quantum batteries.

Additionally, the stability and usability of energy stored in quantum batteries, quantified through measures like ergotropy and quantum Fisher information, are critical to understanding their practical utility. The interplay between coherence, entanglement, and macroscopic usability of stored energy persists as an active area of investigation, necessitating further exploration of decoherence and its mitigation in practical setups.

Implications and Future Directions

The paper outlines substantial progress in the theoretical modeling of both QTMs and quantum batteries, with implications for advancements in quantum thermodynamics and quantum technologies at large. Potential applications extend into quantum metrology and sensing, where QTMs and modified battery constructions can perform high precision measurements under the laws dictated by quantum mechanics.

Moreover, the interplay between quantum phenomena like coherence and entanglement and their implications on thermodynamics at quantum scales continues to inspire the development of new quantum machines and algorithms. The future will likely witness an escalation in the experimental realization of these devices, furthering the knowledge gained from theoretical explorations to widely applicable technological innovations.