Volume 143, Number 2, July 2023
|Number of page(s)||5|
|Published online||24 July 2023|
On the lower bound of the Heisenberg uncertainty product in the Boltzmann states
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China - Hefei, Anhui 230026, China
(a) E-mail: firstname.lastname@example.org (corresponding author)
Received: 20 May 2023
Accepted: 11 July 2023
The uncertainty principle lies at the heart of quantum mechanics, as it describes the fundamental trade-off between the precision of position and momentum measurements. In this work, we study the quantum particle in the Boltzmann states and derive a refined lower bound on the product of and . Our new bound is expressed in terms of the ratio between and the thermal de Broglie wavelength, and provides a valuable tool for characterizing thermodynamic precision. We apply our results to the Brownian oscillator system, where we compare our new bound with the well-known Heisenberg uncertainty principle. Our analysis shows that our new bound offers a more precise measure of the thermodynamic limits of precision.
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