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

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 Δx and Δp. Our new bound is expressed in terms of the ratio between Δx 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.

References in corpus (5)

• Heisenberg's Uncertainty Principle
• Experimental noise filtering by quantum control
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Retrodiction beyond the Heisenberg uncertainty relation
• Thermodynamic Uncertainty Relations for Steady-State Thermodynamics