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Title: Autonomous machines and clocks in quantum thermodynamics
Author: Frenzel, Max
ISNI:       0000 0004 6348 3345
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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Thermodynamics is one of the core disciplines of physics, and despite its long history it is still a very active area of research. Particularly in the regime of non-equilibrium processes and at small scales many open questions remain. In this thesis we critically study the role that autonomous machines play in the emerging field of quantum thermodynamics. We show that autonomous machines generally comprise several interacting subsystems that can take on various roles. In Part I we look at the issue of external control. Any non-autonomous machine by definition requires some external agent to interact with the machine. This agent is generally assumed to be classical and to not suffer any back-actions from the machine. If all the involved systems are of microscopic size this approximation is no longer valid and we have to include all the control mechanisms within a unified quantum framework. We show that in order to avoid external control and operate autonomously, a machine that is to extract work from another system requires an inbuilt quantum clock. Being itself a finite-size quantum system, such a clock will inevitably experience back-actions and develop correlations with the other systems, which lead to its degradation as a time keeping device. We show that this degradation can be counteracted by a judicious choice of quantum measurements. These measurements not only allow us to stabilise the clock, but also magnify thermodynamic properties such as work from the quantum scale, where their definition can be ambiguous, to the well understood classical scale. In Part II we consider the scenario of an autonomous quantum machine interacting with a thermal environment, for which we are experimentally restricted to only observe a subset of all the possible environment interactions, while the remaining ones are hidden from direct observation. Using a modification of the notion of quantum jump trajectories we show that the visible interactions in many cases still allow us to make some inferences about the hidden interactions. We introduce a new quantity, the coarse-grained hidden entropy, which quantifies the entropy production in the hidden subsystem conditioned on our observations of the visible part. The total entropy production consisting of the sum of visible and coarse-grained hidden entropy is shown to satisfy an integral fluctuations theorem. Depending on the information flow between the subsystems, the hidden entropy can assume negative values in which case the hidden systems acts as a Maxwell's demon. This behaviour is also captured by a modified second law like inequality which gives a refinement of the conventional second law for autonomous quantum machines with continuous information flows between the machine's subsystems.
Supervisor: Jennings, David ; Rudolph, Terry Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral