Title:

Work, heat, and power of quantum processes

The central purpose of this thesis is to study the familiar processes of quantum information theory from a thermodynamic point of view. Chapter 1 introduces equilibrium thermodynamics and its laws. The laws are then motivated in a statistical mechanics approach which explicitly employs the language of quantum information theory. Chapter 2 is dedicated to the concept of work extraction, in particular in non equilibrium scenarios. In this context a generalised notion of equilibrium called passivity is introduced. The chapter's final section gives an introduction and an overview of various approaches to work extraction ranging from classical to explicitly quantum scenarios. Chapter 3 considers the question of powerful unitary operations. Focussing on the case of qubits (or rather wits, short for 'work bits') the chapter's first result is an explicit protocol for maximally powerful driving for any given initial state. Building onto this, the chapter's second main result is a proof that the evolution time (and hence the power of the corresponding work deposition process) can be decreased by a factor of 1/N for an array of N wits if global driving is permitted (rather than individual driving in parallel). Lastly, the thermodynamics of completelypositive and tracepreserving (CPTP) maps is considered in Chapter 4. It is shown that the energy change during such a process can be split into three parts: a worklike equilibrium contribution, a heatlike equilibrium contribution, and a third genuinely nonequilibrium energy difference. All three terms obtain their meaning when considering how much work can be extracted from the input and output state of the CPTP process, respectively. Furthermore, the identification of work and heat in this manner complies with a recently published version of the second law, which applies to the same class of processes. This is demonstrated by considering unital and thermal maps.
