Non-equilibrium thermodynamics and dynamics of quantum systems

Abstract

This thesis is a study of non-equilibrium phenomena in quantum systems. Emphasis is given to the recently derived non-equilibrium fluctuation theorems, which relate the non-equilibrium response of a system to its equilibrium thermodynamic properties. We investigate the validity and importance of these theorems, from both a theoretical and experimental perspective, in systems ranging from a single atom to an ensemble of interacting particles. We also investigate the potential role of quantum dynamics in biological processes. The rest of this thesis is structured as follows; In Ch. 1 we provide an introduction to non-equilibrium thermodynamics in quantum systems. In Ch. 2 we characterise the thermodynamics of the transverse Ising model and use this to provide an analytic verification of the non-equilibrium fluctuation theorems in a quenched quantum many-body system. In Ch. 3 we propose an experimental scheme for measuring the full non-equilibrium statistics of work. We demonstrate our proposal with numerical simulations of a Ca trapped ion experiment and show that it can be used to empirically confirm the quantum fluctuation theorems. In Ch. 4 we develop a model of biological electron transport based on a quantum master equation. We apply our model to respiratory complex I, an enzyme with one of the longest electron transport chains in biology. Finally, in Ch. 5 we discuss potential extensions of the results from the preceding chapters.