Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

260
In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
260
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

697
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
697
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

113
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
113
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

121
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
121
Forced Oscillations01:06

Forced Oscillations

6.7K
When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
6.7K
Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

307
In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
307

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Strong-damping limit of quantum Brownian motion in a disordered environment.

Physical review. E·2026
Same author

Integrating Fluorescent Nanodiamonds into Polymeric Microstructures Fabricated by Two-Photon Polymerization.

Nanomaterials (Basel, Switzerland)·2023
Same author

Shortcuts to Thermodynamic Quasistaticity.

Physical review letters·2022
Same author

Spectroscopic characterization of rare events in colloidal particle stochastic thermodynamics.

Frontiers in chemistry·2022
Same author

Kibble-Zurek Scaling from Linear Response Theory.

Entropy (Basel, Switzerland)·2022
Same author

Fluctuation theorem for irreversible entropy production in electrical conduction.

Physical review. E·2022

Related Experiment Video

Updated: Aug 13, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K

Performance of optimal linear-response processes in driven Brownian motion far from equilibrium.

Lucas P Kamizaki1,2, Marcus V S Bonança1, Sérgio R Muniz2

  • 1Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, 13083-859 Campinas, São Paulo, Brazil.

Physical Review. E
|January 21, 2023
PubMed
Summary

Optimal linear-response processes show strong performance even far from equilibrium. These findings are relevant for experiments using optical tweezers and assessing theoretical methods.

More Related Videos

Optical Trap Loading of Dielectric Microparticles In Air
08:57

Optical Trap Loading of Dielectric Microparticles In Air

Published on: February 5, 2017

9.1K
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.5K

Related Experiment Videos

Last Updated: Aug 13, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.6K
Optical Trap Loading of Dielectric Microparticles In Air
08:57

Optical Trap Loading of Dielectric Microparticles In Air

Published on: February 5, 2017

9.1K
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.5K

Area of Science:

  • Statistical Mechanics
  • Non-Equilibrium Thermodynamics
  • Soft Matter Physics

Background:

  • Brownian motion is fundamental to understanding particle dynamics.
  • Linear-response theory provides approximations for systems near equilibrium.
  • Optimal processes are crucial for efficient energy transfer in physical systems.

Purpose of the Study:

  • To evaluate the performance of optimal linear-response processes far from equilibrium.
  • To compare analytical solutions with numerical simulations in the overdamped regime.
  • To assess the applicability of perturbative methods for irreversible work calculations.

Main Methods:

  • Extensive numerical analysis of driven Brownian motion.
  • Focus on the overdamped regime with known analytical optimal processes.
  • Comparison of linear-response optimal processes with exact solutions using experimental parameters.

Main Results:

  • Optimal linear-response processes demonstrate surprisingly good performance beyond their expected range of validity.
  • A performance metric was developed to compare approximate and exact optimal solutions.
  • The study validates the relevance of these processes for optical tweezer experiments.

Conclusions:

  • Linear-response theory can offer effective strategies for non-equilibrium processes.
  • Perturbative methods for irreversible work may be more accurate than previously thought.
  • The findings bridge theoretical predictions with experimental realities in soft matter systems.