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

Second Law of Thermodynamics02:49

Second Law of Thermodynamics

28.4K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
28.4K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

1.2K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.2K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

948
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
948
Entropy02:39

Entropy

37.8K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
37.8K
Entropy01:18

Entropy

3.8K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.8K
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

7.2K
Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
7.2K

You might also read

Related Articles

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

Sort by
Same author

Molecular Surface Chemistry Drives Anomalous Clustering of Ultrasmall Silica Nanoparticles.

The journal of physical chemistry letters·2026
Same author

Comment on "Discontinuous codimension-two bifurcation in a Vlasov equation".

Physical review. E·2026
Same author

Brownian dynamics simulations of electric double-layer capacitors with tunable metallicity.

The Journal of chemical physics·2026
Same author

Interaction between charged nanoparticles in deionized suspensions.

The Journal of chemical physics·2026
Same author

Forces between charge regulated surfaces inside an electrolyte solution.

The Journal of chemical physics·2025
Same author

Efficient method for simulating ionic fluids between polarizable metal electrodes.

The Journal of chemical physics·2024

Related Experiment Video

Updated: Mar 29, 2026

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

9.1K

Chaos and relaxation to equilibrium in systems with long-range interactions.

Felipe L Antunes1, Fernanda P C Benetti1, Renato Pakter1

  • 1Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary

Systems with long-range interactions can get stuck in nonequilibrium stationary states. Chaotic dynamics, particularly weak chaos, surprisingly accelerates the system's eventual relaxation to thermodynamic equilibrium.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

687
Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments
09:25

Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments

Published on: November 1, 2024

3.0K

Related Experiment Videos

Last Updated: Mar 29, 2026

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

9.1K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

687
Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments
09:25

Author Spotlight: Exploring Intrinsically Disordered Protein Dynamics Through NMR Relaxation Experiments

Published on: November 1, 2024

3.0K

Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Systems with long-range interactions often fail to reach thermodynamic equilibrium, instead entering long-lived nonequilibrium stationary states.
  • These quasistationary states (QSS) have lifetimes that increase with system size, diverging in the thermodynamic limit.
  • Understanding the factors influencing the duration of QSS is crucial for comprehending system dynamics.

Purpose of the Study:

  • To investigate the influence of chaotic dynamics on the lifetime of quasistationary states (QSS) in systems with long-range interactions.
  • To quantify the relationship between the strength of chaos and the rate of relaxation to thermodynamic equilibrium.
  • To determine whether different regimes of chaos impact relaxation times differently.

Main Methods:

  • Analysis of systems with long-range interactions in the thermodynamic limit and for finite particle numbers.
  • Characterization of chaotic dynamics using Lyapunov exponents.
  • Measurement of the time scale for relaxation from QSS to thermodynamic equilibrium.

Main Results:

  • Chaotic dynamics were found to promote faster relaxation from QSS to thermodynamic equilibrium.
  • A surprising inverse relationship was observed: weaker chaos led to faster relaxation compared to stronger chaos.
  • The lifetime of QSS is shown to be sensitive to the degree of chaoticity within the system.

Conclusions:

  • Chaotic dynamics play a significant role in the relaxation processes of systems trapped in QSS.
  • Weak chaos appears to be more effective than strong chaos in facilitating the transition to thermodynamic equilibrium.
  • These findings offer new insights into the behavior of complex systems and their approach to equilibrium.