Related Experiment Video
Updated: May 25, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Jarzynski equality in van der Pol and Rayleigh oscillators.
1Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan. hideohasegawa@goo.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
The Jarzynski equality approximately holds for van der Pol and Rayleigh oscillators, despite being non-Hamiltonian. Deviations occur near the relaxation oscillation period, with non-Gaussian work distributions observed.
Area of Science:
- Non-equilibrium statistical mechanics
- Complex systems dynamics
Background:
- The Jarzynski equality (JE) is a fundamental theorem in non-equilibrium statistical mechanics.
- Deterministic non-Hamiltonian systems, like van der Pol and Rayleigh oscillators, are not typically expected to satisfy the JE due to irreversibility.
Purpose of the Study:
- To investigate the applicability of the Jarzynski equality in van der Pol and Rayleigh oscillators.
- To analyze the behavior of the work distribution function (WDF) and its dependence on the applied force ramp duration (τ).
Main Methods:
- Numerical simulations of van der Pol and Rayleigh oscillators.
- Calculation of work (W) done by an applied ramp force.
- Analysis of the work distribution function (WDF) and its statistical properties.
Main Results:
- The Jarzynski equality approximately holds for a wide range of ramp durations (τ), except near the relaxation oscillation period (T).
- The work distribution function (WDF) exhibits a non-Gaussian, U-shaped structure for strong damping.
- A semi-quantitative explanation for the τ dependence of R (related to free energy) was derived using a limit-cycle oscillation expression.
Conclusions:
- The Jarzynski equality shows approximate validity in certain deterministic non-Hamiltonian systems, contrary to initial expectations.
- The observed deviations and non-Gaussian WDF highlight the complexities of applying JE to dissipative systems.
- Findings contrast with the rigorous JE satisfaction in the Nosé-Hoover oscillator, another non-Hamiltonian model.
More Related Videos
07:56A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
14:18Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
Published on: February 28, 2016
Related Concept Videos
01:04Oscillations 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...
01:07Damped Oscillations
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
01:28Symmetry in Maxwell's Equations
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
01:30Oscillations In An LC Circuit
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
01:06Forced Oscillations
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.