Energy-temperature uncertainty relation in quantum thermodynamics
Miller, H; Anders, J
Date: 6 June 2018
Article
Journal
Nature Communications
Publisher
Springer Nature
Publisher DOI
Abstract
Much like Heisenberg’s uncertainty principle in quantum mechanics, there exists a thermodynamic
uncertainty relation in classical statistical mechanics that limits the simultaneous estimation of energy
and temperature for a system in equilibrium. However, for nanoscale systems deviations from standard
thermodynamics arise due to ...
Much like Heisenberg’s uncertainty principle in quantum mechanics, there exists a thermodynamic
uncertainty relation in classical statistical mechanics that limits the simultaneous estimation of energy
and temperature for a system in equilibrium. However, for nanoscale systems deviations from standard
thermodynamics arise due to non-negligible interactions with the environment. Here we include interactions
and, using quantum estimation theory, derive a generalised thermodynamic uncertainty relation
valid for classical and quantum systems at all coupling strengths. We show that the non-commutativity
between the system’s state and its effective energy operator gives rise to additional quantum fluctuations
that increase the uncertainty in temperature and modify the heat capacity. Surprisingly, these
quantum fluctuations are described by the average Wigner-Yanase-Dyson skew information, a quantity
intimately connected to measures of coherence. For temperature estimation we demonstrate that the optimal
signal-to-noise ratio is constrained not only by the heat capacity, but an additional dissipative term
arising from the non-negligible interactions. Practically this will inform the design of optimal nanoscale
thermometers. On the fundamental side the results shed light on the interplay between classical and
non-classical fluctuations in quantum thermodynamics.
Physics and Astronomy
Faculty of Environment, Science and Economy
Item views 0
Full item downloads 0