Abstract
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.
- Received 17 November 2014
DOI:https://doi.org/10.1103/PhysRevX.5.021001
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Published by the American Physical Society
Viewpoint
New Entry in the Thermodynamic Rulebook for Quantum Systems
Published 18 November 2015
Thermodynamic laws that are unique to quantum systems in a superposition of states have been derived using an information-theory approach.
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Popular Summary
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. Here, we focus on the property of quantum coherence, the ability of quantum systems to emulate Schrödinger’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. Our work, which is valid at any temperature, relies 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 have found 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.
It has long been appreciated that thermodynamics is subtly interlinked with the notion of information. Our 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.