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Abstract
Autonomous engines operating at the nanoscale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental tradeoff between current fluctuations and entropy production forms the basis of the recently formulated thermodynamic uncertainty relations (TURs). However, these relations have so far only been derived for classical Markovian systems and can be violated in the quantum regime. In this paper we show that the geometry of quantum nonequilibrium steadystates alone, already directly implies the existence of a TUR, but with a looser bound. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennanZubarev ensemble, which provides an exact description of nonequilibrium steadystates. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the quantum CramerRao bound, a fundamental result from parameter estimation theory. By combining techniques from manybody physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines.
Original language  English 

Number of pages  14 
Journal  arXiv 
Publication status  Submitted  29 Jan 2019 
Bibliographical note
6 pages of main text + 7 pages of AppendicesKeywords
 condmat.statmech
 quantph
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Projects
 1 Finished

8102 EPSRC  Emerging correlations from strong driving  EP/P025110/2
24/09/18 → 23/10/19
Project: Research, Parent