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

Dynamic Equilibrium02:20

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
Non-equilibrium in the Cell01:16

Non-equilibrium in the Cell

An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

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...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

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 because...

You might also read

Related Articles

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

Sort by
Same author

Transfer of Active Motion from Medium to Probe via the Induced Friction and Noise.

Physical review letters·2026
Same author

Coupling an elastic string to an active bath: The emergence of inverse damping.

Physical review. E·2025
Same author

Negative specific heats: where Clausius and Boltzmann entropies separate.

Physical chemistry chemical physics : PCCP·2025
Same author

Induced friction on a probe moving in a nonequilibrium medium.

Physical review. E·2025
Same author

Heat capacity of periodically driven two-level systems.

Physical review. E·2024
Same author

Frenetic steering: Nonequilibrium-enabled navigation.

Chaos (Woodbury, N.Y.)·2024
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: May 30, 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

Monotonic return to steady nonequilibrium.

Christian Maes1, Karel Netočný, Bram Wynants

  • 1Instituut voor Theoretische Fysica, K. U. Leuven, Belgium.

Physical Review Letters
|July 30, 2011
PubMed
Summary
This summary is machine-generated.

We introduce a novel Lyapunov function to track relaxation in nonequilibrium systems. This new function, derived from fluctuation analysis, shows consistent monotonic decrease, unlike older methods that oscillate near steady states.

More Related Videos

The Use of Chemostats in Microbial Systems Biology
13:19

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Related Experiment Videos

Last Updated: May 30, 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

The Use of Chemostats in Microbial Systems Biology
13:19

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Dynamical Systems Theory

Background:

  • Understanding the approach to steady states in systems driven far from equilibrium is a fundamental challenge in statistical mechanics.
  • Existing Lyapunov functions, often based on entropy production, can exhibit oscillations near steady states, complicating analysis.
  • Characterizing the dynamics of relaxation is crucial for predicting system behavior and stability.

Purpose of the Study:

  • To propose and analyze a new candidate Lyapunov function for general non-equilibrium steady states.
  • To provide a measure of dynamical activity that reliably indicates relaxation.
  • To contrast the behavior of the proposed function with existing methods based on entropy production.

Main Methods:

  • Derivation of the Lyapunov function from the large-time asymptotics of time-symmetric fluctuations.
  • Analysis of driven Markov jump and diffusion processes.
  • Numerical evidence and rigorous arguments for monotonic time dependence.

Main Results:

  • The proposed Lyapunov function measures an excess in dynamical activity rates for driven Markov processes.
  • Demonstrated monotonic time dependence of the function near steady nonequilibrium states.
  • Showcased the function's stability and lack of oscillations, contrasting with entropy-production-based methods.

Conclusions:

  • The novel Lyapunov function provides a robust tool for analyzing relaxation dynamics in non-equilibrium systems.
  • This function offers a more reliable indicator of approach to steady states compared to traditional methods.
  • The findings contribute to a deeper understanding of fluctuation-dissipation theorems and system stability far from equilibrium.