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Quantum Thermodynamic Processes: Energy and Information Flow at the Nanoscale

G. Mahler

Published Dec 19, 2014• 15 citations
OpenAlex

Abstract

The point of departure of this book is a triad of themes: information theory, thermodynamics, and quantum mechanics. These are related: thermodynamics and quantum mechanics form the basis of quantum thermodynamics; information and quantum mechanics underly, inter alia, the notorious quantum measurement problem; and information and thermodynamics have much to say about control limits in the tension between micro- and macro-descriptions.Why does the world around us typically look thermal-from cosmology down to individual embedded spins? Do informational measures constitute additional (independen

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The point of departure of this book is a triad of themes: information theory, thermodynamics, and quantum mechanics. These are related: thermodynamics and quantum mechanics form the basis of quantum thermodynamics; information and quantum mechanics underly, inter alia, the notorious quantum measurement problem; and information and thermodynamics have much to say about control limits in the tension between micro- and macro-descriptions.Why does the world around us typically look thermal-from cosmology down to individual embedded spins? Do informational measures constitute additional (independen
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.
This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text, aimed at graduate level physics students with a working knowledge of quantum mechanics and statistical physics, provides a brief overview of the development of classical thermodynamics and its quantum formulation in Chapter 1. Chapter 2 then explores typical thermodynamic settings, such as cycles and work extraction protocols, when the working material is genuinely quantum. Finally, Chapter 3 explores the thermodynamics of quantum information processing and introduces the reader to some more state-of-the-art topics in this exciting and rapidly developing research field.
Although it is 70 years old, there are still areas of quantum theory which are open to interpretation. This book deals with such interpretational problems, and in particular with the issue of the measurement process. The main theme is whether quantum mechanics can be viewed as a (semantically) complete theory, namely as a theory capable of describing not only the physical object under observation but also the measuring instruments used to detect the properties of that physical object. The problematic aspects arise from the fact that the measuring instruments themselves behave as classical physical systems. Thus, we are faced with the open problem of the transition from the quantum to the classical, or more explicitly, the problem of why the composition of many quantum micro-objects gives rise to classical macro-objects. This book goes carefully, exhaustively, and deeply into the interpretational problems of quantum mechanics induced by the measurement process. The solution of many relevant issues, as well as the problems that remain unsolved, emerge clearly. The discussion itself is self-contained and the technical parts are reader-friendly. This book is of value to graduate students and researchers who have an interest in the physical, mathematical, and philosophical foundations of quantum mechanics.
Planck found, when attempting to describe the way in which hot bodies glow, that energy at microscopic scales often comes in discrete chunks. Thus began the long and intimate relationship between the field of thermodynamics, which explores our ability to manipulate heat and other energy transfers between macroscopic systems, and quantum mechanics, which explains the dynamics of individual microscopic systems. Even as both our technology and our theoretical investigations have extended to ever-smaller devices, our understanding of quantum effects on thermodynamics has remained almost exclusively limited to the quantized nature of energy. There is much more, however, to quantum theory than energy quantization. In this thesis we focus on the property of quantum coherence, the ability of quantum systems to emulate Schrodinger’s cat and somehow be neither dead nor alive, but something completely different altogether. We provide a simple and elegant formulation for the processing of coherence in thermodynamics, relying on the fact that thermodynamical processes possess an underlying time-translation symmetry. This fact allows us to quantify the ways in which coherence can play an active role, facilitating otherwise impossible thermodynamic transformations. We argue that coherence should be thought of as a distinctly quantum-mechanical thermodynamic resource. By considering an isolated quantum system connected, for some period of time, to a thermal bath, we give fundamental limitations on how coherence can be irreversibly manipulated. These limitations are related to those dictated on energy transfer by the second law of thermodynamics. Others topics that are investigated here is what is the role of correlations at the smallest scales and the conversion of quantum coherence into work. It has long been appreciated that thermodynamics is subtly interlinked with the notion of information. This work provides evidence that, to apply the laws of thermodynamics to the smallest systems around us, we must develop deeper insights into the nature of quantum information.