Position-Momenta Uncertainties in Classical Systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908674597847040 |
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| author | Singh, Dipesh K. Mohanty, P. K. |
| author_facet | Singh, Dipesh K. Mohanty, P. K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_24122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Position-Momenta Uncertainties in Classical Systems Singh, Dipesh K. Mohanty, P. K. Statistical Mechanics Quantum Physics 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. |
| title | Position-Momenta Uncertainties in Classical Systems |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2503.24122 |