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Related Experiment Video

Updated: May 11, 2025

Optical Trap Loading of Dielectric Microparticles In Air

Optical Trap Loading of Dielectric Microparticles In Air

Published on: February 5, 2017

Minimal work protocols for inertial particles in nonharmonic traps.

Julia Sanders¹, Marco Baldovin², Paolo Muratore-Ginanneschi¹

¹University of Helsinki, Department of Mathematics and Statistics, 00014 Helsinki, Finland.

Physical Review. E

|April 18, 2025

Summary

We developed a numerical method for optimal control of nanoscale systems with inertia, achieving target states with minimal energy. This method handles complex conditions, revealing unique dynamics compared to simpler models.

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Area of Science:

Statistical physics and thermodynamics
Nanoscale control systems
Computational physics

Background:

Miniaturized technology enables precise control of nanoscale physical systems.
Control problems in stochastic thermodynamics focus on reaching target states with minimal energy cost.
Previous work established methods for optimal control, but often in simplified (overdamped) regimes.

Purpose of the Study:

To develop a numerical method for optimal control of nanoscale particles considering inertia.
To find optimal control protocols for non-Gaussian initial/final conditions and nonharmonic confinements.
To analyze the dynamics and energy costs in the underdamped regime compared to the overdamped limit.

Main Methods:

Numerical simulation of a particle subject to thermal fluctuations and inertia.
Extension of previous work to handle non-Gaussian initial and final conditions.
Analysis of time-dependent position and momentum distributions, and entropy production.

Main Results:

A numerical method for optimal control in the underdamped regime is provided.
The underdamped regime exhibits qualitatively different dynamics and broken symmetries compared to the overdamped limit.
Momentum mean stabilizes, while position and second moments evolve non-trivially; optimal entropy production bounds are confirmed as tight in the adiabatic limit.

Conclusions:

Inertia significantly alters optimal control strategies and system dynamics at the nanoscale.
The developed numerical method allows for precise control under more realistic, complex conditions.
Findings contribute to understanding energy efficiency and control in stochastic thermodynamic systems.