2011/04/30 by Hideo Hasegawa
Mathematics · Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Hamiltonian (control theory) #Hamiltonian system #Mathematical physics #Mathematics #Neural dynamics and brain function #Physics #Quantum mechanics #Van der Pol oscillator #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.84.061112
published as Phys. Rev. E 84 (2011) 061112 · 20 pages, 13 figures; the final version accepted in Phys. Rev. E
arxiv created 2011/11/23 · openalex publication_date 2011/12/07 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 reversible. Our simulations that calculate the contribution to the work W of an applied ramp force with a duration \ensuremathτ show that the JE approximately holds for a fairly wide range of \ensuremathτ including \ensuremathτ\ensuremath→0 and \ensuremathτ\ensuremath→\ensuremath∞, except for \ensuremathτ\ensuremath∼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 \ensuremathτ dependence of R (=\ensuremath-kBTln\ensuremath⟨e^\ensuremath-\ensuremathβW\ensuremath⟩) obtained by our simulations is semiquantitatively elucidated with the use of a simple expression for limit-cycle oscillations, where the bracket \ensuremath⟨\ifmmode⋅\else\textperiodcentered\fi\ensuremath⟩ 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.