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 $c=\frac{1}{2}$ for particles in central potentials.

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• Classical statistical mechanics
• Fluctuations & noise
• Stochastic processes
• Stochastic dynamical systems
• Dissipative particle dynamics
• Fokker–Planck equation
• Langevin equation