Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.
Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.
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.
The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow-up work in the community.It requires energy-preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm.So far, such unitary operations have been considered a "free" resource in the theory.However, this is only an idealization of a necessarily inexact process.Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning an interaction "on or off."However, the control system will inevitably be degraded by the backaction caused by the implementation of the unitary.We derive conditions on the quality of the control device so that the laws of thermodynamics do not change and prove-by utilizing a good quantum clock-that the laws of quantum mechanics allow the backreaction to be small enough so that these conditions are satisfiable.Our inclusion of nonidealized control into the resource framework also raises interesting prospects, which were absent when considering idealized control.Among other things, the emergence of a third law without the need for the assumption of a light cone.Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource-theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.
We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we show that this model can exactly implement any energy-conserving unitary on the engine, without degrading the clock. Furthermore, we show that when the engine includes a quantum work storage device we can approximately perform completely general unitaries on the remainder of the engine. This framework can be used in quantum thermodynamics to carry out arbitrary transformations of a system, with accuracy and extracted work as close to optimal as desired, while obeying the first and second laws of thermodynamics. We thus show that autonomous thermal machines suffer no intrinsic thermodynamic cost compared to externally controlled ones.
We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we show that this model can exactly implement any energy-conserving unitary on the engine, without degrading the clock. Furthermore, we show that when the engine includes a quantum work storage device we can approximately perform completely general unitaries on the remainder of the engine. This framework can be used in quantum thermodynamics to carry out arbitrary transformations of a system, with accuracy and extracted work as close to optimal as desired, while obeying the first and second laws of thermodynamics. We thus show that autonomous thermal machines suffer no intrinsic thermodynamic cost compared to externally controlled ones.
The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow up work in the community. It requires energy preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a free resource of the theory. However, this is only an idealisation of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning on/off an interaction. However, the control system will inevitable be degraded by the back-action caused by the implementation of the unitary. We derive conditions on the quality of the control device so that the laws of thermodynamics do not change; and prove --- by utilising a good quantum clock --- that the laws of quantum mechanics allow the back-reaction to be small enough so that these conditions are satisfiable. Our inclusion of non-idealised control into the resource framework also rises interesting prospects, which were absent when considering idealised control. Namely: 1) the emergence of a 3rd law --- without the need for the assumption of a light-cone. 2) the inability to apply the 2nd laws out of equilibrium.
Our results and framework unify the field of autonomous thermal machines with the thermodynamic quantum resource theoretic one, and lay the groundwork for all quantum processing devices to be unified with fully autonomous machines.
There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific thermodynamic primitive, such as work extraction in the presence of a thermal environment, while having minimal or no control from the macroscopic regime. Beyond experimental implementations, this provides an arena in which to address certain foundational aspects such as the role of coherence in thermodynamics, the use of clock degrees of freedom and the simulation of local time-dependent Hamiltonians in a particular quantum subsystem. For small-scale systems additional issues arise. Firstly, it is not clear to what degree genuine ordered thermodynamic work has been extracted, and secondly non-trivial back-actions on the thermal machine must be accounted for. We find that both these aspects can be resolved through a judicious choice of quantum measurements that magnify thermodynamic properties up the ladder of length-scales, while simultaneously stabilising the quantum thermal machine. Within this framework we show that thermodynamic reversibility is obtained in a particular Zeno limit, and finally illustrate these concepts with a concrete example involving spin systems.