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arXiv · 2503.24122

Position-Momenta Uncertainties in Classical Systems

Dipesh K. Singh·P. K. Mohanty
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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.

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BibTeXRIS

Dipesh K. Singh, P. K. Mohanty. 2025-03-31. Position-Momenta Uncertainties in Classical Systems. https://doi.org/10.1103/6pj3-7df9

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