Font Size:
Fluctuation theorems for the undriven Duffing oscillator
##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-10 12:00 PM – 03:45 PM
Last modified: 2019-06-14
Abstract
Undamped autonomous nonlinear systems with one degree of freedom are described by a Hamiltonian H(x,p)=[p^2+V(x)]⁄2m. When their damping is of the form γp, we prove by two methods that H(x,p)⁄γ is a global Lyapunov function. We exploit this result to verify the Jarzynski relation past the pitchfork bifurcation of the undriven Duffing oscillator.
Along the first method, we also obtain the explicit form of a detailed fluctuation theorem, γD[ln(p_r^F)-ln(p_r^B)]=[(d_tx)^2⁄2+V](t_f)-[(d_tx)^2⁄2+V](t_i), analog to TΔS=ΔU. Here D is the noise intensity, and p_r^F, p_r^B the forward and backward probabilities of a given trajectory in configuration space. We verify numerically this theorem for the undriven Duffing oscillator, to within an error of order 10^{-7}.
Along the first method, we also obtain the explicit form of a detailed fluctuation theorem, γD[ln(p_r^F)-ln(p_r^B)]=[(d_tx)^2⁄2+V](t_f)-[(d_tx)^2⁄2+V](t_i), analog to TΔS=ΔU. Here D is the noise intensity, and p_r^F, p_r^B the forward and backward probabilities of a given trajectory in configuration space. We verify numerically this theorem for the undriven Duffing oscillator, to within an error of order 10^{-7}.