Nelly Ng: The fundamental limits of efficiency for quantum heat engines

The speaker from the University of Berlin is introduced to discuss quantum thermodynamics, specifically focusing on the theoretical limits of efficiency for quantum heat engines. The talk is set against the backdrop of a conference that has extensively covered information theory and its applications in thermodynamics. The speaker outlines the joint work with Lucia Woods and Stephanie, emphasizing the evolution of thermodynamics from macroscopic systems to the mesoscopic regime, which includes non-equilibrium processes. The goal is to explore the fundamental efficiency limits of quantum heat engines within this framework.

The speaker delves into the essence of quantum thermodynamics, highlighting the unique features of quantum systems such as small size, finite energy dimensions, and the presence of quantum effects like coherence and entanglement. The talk also provides concrete examples of quantum machines that experimentalists are interested in, such as a quantum refrigerator and a trapped ion system, to illustrate the practical applications of quantum thermodynamics. The speaker emphasizes the importance of understanding the efficiency of quantum heat engines in the context of quantum computation and other quantum technologies.

The speaker presents a theoretical framework for analyzing quantum heat engines, starting with a discussion on the conditions and mechanisms for quantum states to equilibrate. The focus then shifts to the energy cost of computations and information processing, the role of coherence and entanglement in quantum systems, and the usefulness of quantum heat engines. The speaker aims to apply the resource steering framework to construct a generic model of quantum heat engines and evaluate their theoretical efficiency limits.

A significant portion of the talk is dedicated to the challenge of defining work in quantum thermodynamics. The speaker discusses various perspectives, including the information theory approach, the axiomatic approach, and the use of resource theories to quantify work. The talk also addresses the difficulty in distinguishing between heat and work in quantum systems due to their small energy scales and the presence of thermal fluctuations, leading to a range of different classifications for work extraction in the quantum regime.

The concept of catalysis in quantum thermodynamics is explored, with the speaker explaining how catalysts can be used to facilitate state transitions in quantum systems. The talk differentiates between exact catalysis, where the catalyst returns to its original state without any correlation with the system, and inexact catalysis, which allows for small errors in the final state of the catalyst. The speaker also discusses the implications of these concepts for the implementation of quantum processes in experimental settings.

The speaker provides an in-depth analysis of quantum heat engines within the framework of catalysis, discussing how to apply resource theories to build and study these engines. The focus is on using a cold bath as a system of interest and attaching a battery to extract work. The speaker outlines the assumptions of the setup, including the initial state of the systems and the use of catalytic operations to achieve work extraction.

The talk moves towards understanding the maximum achievable efficiency of quantum heat engines. The speaker discusses the use of free energy and generalized free energies as constraints to determine the efficiency limits. The analysis reveals that the Carnot efficiency serves as an upper bound for the efficiency that can be achieved under certain conditions, such as the quasi-static limit, which is defined within the resource theory framework.

The speaker distinguishes between perfect work, where the increase in entropy of the battery is zero, and near-perfect work, which allows for a small increase in entropy. The analysis shows that while perfect work is not possible under the generalized second laws, near-perfect work can sometimes achieve the Carnot efficiency. The speaker also discusses the conditions under which these efficiencies can be achieved, highlighting the importance of the initial and final states of the cold bath.

The talk concludes with a discussion on the impact of different work definitions on the efficiency of quantum heat engines. The speaker emphasizes that the definition of work is crucial, as it can lead to different interpretations of efficiency, especially when considering imperfect work. The speaker also presents examples where the efficiency can exceed the Carnot efficiency under certain conditions, suggesting that the understanding of work in quantum thermodynamics may need further refinement.

The speaker acknowledges open questions and suggests future directions for research in quantum thermodynamics. There is a call for a clearer understanding of work in quantum systems and the exploration of more realistic thermodynamical models. The speaker also highlights the need to bridge the gap between theoretical work and experimental practice, encouraging further research to connect the resource theory framework with experimental scenarios in quantum thermodynamics.

The final part of the script includes a question and answer session with the audience. The speaker addresses queries related to the framework of quantum thermodynamics, the realistic scenarios where these results could apply, and the implications of different work definitions on the efficiency of quantum heat engines. The discussion delves into the nuances of the resource theory approach and its connection to experimental settings, reflecting the ongoing dialogue between theory and practice in the field of quantum thermodynamics.