Abstract
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. However, for nanoscale systems deviations from standard thermodynamics arise due to their interactions with the environment. Here we include such 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 quantum fluctuations that increase the temperature uncertainty. Surprisingly, these additional fluctuations are described by the average Wigner-Yanase-Dyson skew information. We demonstrate that the temperature’s signal-to-noise ratio is constrained by the heat capacity plus a dissipative term arising from the non-negligible interactions. These findings shed light on the interplay between classical and non-classical fluctuations in quantum thermodynamics and will inform the design of optimal nanoscale thermometers.
Highlights
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large
Hamiltonian question the validity of Eq (1) for general classical and quantum systems, and the aim of this paper is to investigate the impact of strong coupling on the thermodynamic uncertainty relation
We demonstrate that the skew information is linked to the heat capacity of the system through a modified fluctuation-dissipation relation (FDR)
Summary
It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. For nanoscale systems deviations from standard thermodynamics arise due to their interactions with the environment We include such 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 quantum fluctuations that increase the temperature uncertainty. We demonstrate that the temperature’s signal-to-noise ratio is constrained by the heat capacity plus a dissipative term arising from the non-negligible interactions These findings shed light on the interplay between classical and non-classical fluctuations in quantum thermodynamics and will inform the design of optimal nanoscale thermometers. To assign a sharp energy to the system it must be isolated from the reservoir, rendering the system’s temperature T uncertain Based on this heuristic argument Bohr conjectured the thermodynamic uncertainty relation: Δβ. We will see that the internal energy U and its fluctuations ΔU are determined by a modified internal energy oopf etrhaetosry, sdteenmo3t5e,d39.byThE^iSÃs, that differs from the modification brings bare into
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