On the lower bound of the Heisenberg uncertainty product in the Boltzmann states

Yao Wang

doi:10.1209/0295-5075/ace64f

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arXiv · 2308.07613

On the lower bound of the Heisenberg uncertainty product in the Boltzmann states

Yao Wang

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Abstract

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 {\Delta}x and {\Delta}p. Our new bound is expressed in terms of the ratio between {\Delta}x 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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Yao Wang. 2023-08-15. On the lower bound of the Heisenberg uncertainty product in the Boltzmann states. https://doi.org/10.1209/0295-5075%2Face64f

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