Position-Momenta Uncertainties in Classical Systems

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.

9 pages, 4 figures, Supplemental Material

References in corpus (17)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Dissipation bounds all steady-state current fluctuations
• Circular motion of asymmetric self-propelling particles
• Universal trade-off relation between power and efficiency for heat engines
• Gravitaxis of asymmetric self-propelled colloidal particles
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Dynamics of a self-propelled particle in a harmonic trap
• Extraction of work from a single thermal bath in the quantum regime
• Unified thermodynamic uncertainty relations in linear response
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Long time position distribution of an active Brownian particle in two dimensions
• Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials
• Direct Route to Thermodynamic Uncertainty Relations and Their Saturation
• R. Fürth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift für Physik,} \textbf{81} 143-162]
• Experimental realization of an analog of entanglement between two Brownian particles