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 2014DOI:https://doi.org/10.1103/PhysRevX.5.021001This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society
Highlights
Fundamental laws of nature often take the form of restrictions: nothing can move faster than light in vacuum; energy cannot be created from nothing; there are no perpetuum mobiles
A natural question to ask is, what amounts to a resource when we are restricted by these laws? This question is interesting in the context of small quantum systems in the emergent field of single-shot thermodynamics [2,3,4,5,6,7,8,9,10]
The central question of thermodynamics is, what are the allowed transformations of a system that are consistent with the first and second laws? Many of the developments in single-shot thermodynamics have been restricted to quantum states that do not possess quantum coherence between energy eigenspaces [4,5,6,12], and recent analysis has shown that a whole family of independent entropic
Summary
Fundamental laws of nature often take the form of restrictions: nothing can move faster than light in vacuum; energy cannot be created from nothing; there are no perpetuum mobiles. The first and second laws are fundamental constraints in thermodynamics These force thermodynamic processes to conserve the overall energy and forbid free conversion of thermal energy into work. Coherence can be viewed as a second, independent resource in thermodynamics [13] This stems from the fact that energy conservation, implied by the first law, restricts the thermodynamic processing of coherence. Since coherence is a thermodynamic resource, an open question is what kind of coherence processing is allowed by thermodynamic means This foundational question is of interest for future advancements in nanotechnology, as interference effects are relevant [14,15] at scales we are increasingly able to control [16,17,18,19,20].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
