The Jarzynski equality in van der Pol and Rayleigh oscillators

Details The Jarzynski equality in van der Pol and Rayleigh oscillators The Jarzynski equality in van der Pol and Rayleigh oscillators

2011-04-25

arxiv.org/abs/1104.4756v3

Phys. Rev. E 84 (2011) 061112

Physics

Condensed Matter

Statistical Mechanics

20 pages, 13 figures; the final version accepted in Phys. Rev. E

Scientific paper

We have studied the Jarzynski equality (JE) in van der Pol and Rayleigh oscillators which are typical deterministic non-Hamiltonian models, but not expected to rigorously satisfy the JE because they are not microscopically reversible. Our simulations that calculate the contribution to the work $W$ of an applied ramp force with a duration $\tau$ show that the JE approximately holds for a fairly wide range of $\tau$ including $\tau \rightarrow 0 $ and $\tau \rightarrow \infty$, except for $\tau \sim T$ where $T$ denotes the period of relaxation oscillations in the limit cycle. The work distribution function (WDF) is shown to be non-Gaussian with the $U$-shaped structure for a strong damping parameter. The $\tau$ dependence of $R$ $(=- k_B T \ln)$ obtained by our simulations is semi-quantitatively elucidated with the use of a simple expression for limit-cycle oscillations, where the bracket $<\cdot>$ expresses an average over the WDF. The result obtained in self-excited oscillators is in contrast with the fact that the JE holds in the Nos\'{e}-Hoover oscillator which also belongs to deterministic non-Hamiltonian models.

Affiliated with

Also associated with

No associations

Rating

The Jarzynski equality in van der Pol and Rayleigh oscillators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Jarzynski equality in van der Pol and Rayleigh oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Jarzynski equality in van der Pol and Rayleigh oscillators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-545416