Position-Momenta Uncertainties in Classical Systems

• URL: http://arxiv.org/abs/2503.24122v1
• Date: Mon, 31 Mar 2025 14:08:41 GMT
• Title: Position-Momenta Uncertainties in Classical Systems
• Abstract summary: We show that classical particles immersed in such baths exhibit position-momentum uncertainties.<n>The proportionality constant, $c$, is dimensionless and independent of the system's parameters.
• Score: 0.6445605125467574
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 independent of 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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