Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.
Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state, we arrive at an additional, independent set of thermodynamic constraints that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilárd engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and the theory of entanglement.
Recent studies have developed fundamental limitations on nanoscale thermodynamics, in terms of a set of independent free energy relations. Here we show that free energy relations cannot properly describe quantum coherence in thermodynamic processes. By casting time-asymmetry as a quantifiable, fundamental resource of a quantum state we arrive at an additional, independent set of thermodynamic laws, that naturally extend the existing ones. These asymmetry relations reveal that the traditional Szilard engine argument does not extend automatically to quantum coherences, but instead only relational coherences in a multipartite scenario can contribute to thermodynamic work. We find that coherence transformations are always irreversible. Our results also reveal additional structural parallels between thermodynamics and entanglement theory.
The principle of superposition is one of the main building blocks of quantum physics and has tremendous consequences both for our fundamental understanding of nature and for technological applications. In particular, the existence of coherent superposition leads to the concept of unavoidable quantum uncertainty. The role played by this "coherent" uncertainty within thermodynamics, as well as its relationship to classical lack of knowledge, is the main subject of this thesis. In Part I we study thermodynamic limitations of processing quantum coherence within a resource-theoretic framework. Using the time-translation symmetry that arises from the first law of thermodynamics, we find constraints on possible manipulations of coherence and prove their irreversibility due to the second law. We also generalise to the quantum domain Szilard's concept of converting information into work. Namely, we show how, in the presence of a heat bath, coherence of a system can be exploited to perform mechanical work. Finally, we analyse the effect that coherence has on the structure of the thermodynamic arrow of time, i.e., on the set of states into which a given state can freely evolve under thermodynamic constraints. In Part II we focus on the interplay between quantum and classical uncertainty manifested in uncertainty relations. We show that separating the total uncertainty into these two distinct components leads to a new type of "fixed-entropy" uncertainty relation. We also analyse how classical ignorance affects the structure of states that minimise the unavoidable uncertainty arising from the noncommutativity of two observables. Finally, we study error-disturbance trade-off relations and, by proving that quantum uncertainty can be simultaneously maximised for any two observables, we clarify the unphysical nature of state-dependent relations.
In the classical regime, thermodynamic state transformations are governed by the free energy. This is also called as the second law of thermodynamics. Previous works showed that, access to a catalytic system allows us to restore the second law in the quantum regime when we ignore coherence. However, in the quantum regime, coherence and free energy are two independent resources. Therefore, coherence places additional nontrivial restrictions on the state transformations that remain elusive. In order to close this gap, we isolate and study the nature of coherence, i.e., we assume access to a source of free energy. We show that allowing catalysis along with a source of free energy allows us to amplify any quantum coherence present in the quantum state arbitrarily. Additionally, any correlations between the system and the catalyst can be suppressed arbitrarily. Therefore, our results provide a key step in formulating a fully general law of quantum thermodynamics.
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.
The first law of thermodynamics imposes not just a constraint on the energy content of systems in extreme quantum regimes but also symmetry constraints related to the thermodynamic processing of quantum coherence. We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state. We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature. We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy. Moreover, the recently developed thermomajorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis. Published by the American Physical Society 2015
The first law of thermodynamics imposes not just a constraint on the energy content of systems in extreme quantum regimes but also symmetry constraints related to the thermodynamic processing of quantum coherence.We show that this thermodynamic symmetry decomposes any quantum state into mode operators that quantify the coherence present in the state.We then establish general upper and lower bounds for the evolution of quantum coherence under arbitrary thermal operations, valid for any temperature.We identify primitive coherence manipulations and show that the transfer of coherence between energy levels manifests irreversibility not captured by free energy.Moreover, the recently developed thermomajorization relations on block-diagonal quantum states are observed to be special cases of this symmetry analysis.