# Position-Momenta Uncertainties in Classical Systems

Source: [Position-Momenta Uncertainties in Classical Systems](<https://www.sota2.com/research/paper/68fa49d11e209131ce939f57>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-11-27T05:01:19.526Z

Authors: Dipesh K. Singh, P. K. Mohanty

Published: 2025-03-31T14:08:41.000Z

## Abstract

We design a thermal bath that preserves the conservation of a system's angular momentum or allows it to fluctuate around a specified nonzero mean while maintaining a Boltzmann distribution of energy in the steady state. We demonstrate that classical particles immersed in such baths exhibit position-momentum uncertainties with a strictly positive lower bound proportional to the absolute value of the mean angular momentum. The proportionality constant, $c$, is dimensionless and does not depend explicitly on the system's parameters. Remarkably, while $c$ is universally bounded by unity, it attains the exact value $c=1/2$ for particles in central potentials.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2503.24122>)

[PDF](<https://arxiv.org/pdf/2503.24122.pdf>)