Fluctuation theorem for a deterministic one-particle system.

A Duffing oscillator is driven by a sum of N chaotic time series. These time series are solutions of the undriven Duffing equation. It is shown that N=1 is sufficient to render the fluctuation theorem [Phys. Rev. Lett. 74, 2694 (1995)]; J. Math. Phys. 41, 4061 (2000)]; Adv. Phys. 51, 1529 (2002)]] for the power J(tau) averaged within intervals of length tau . In particular, the probabilities p( J(tau) ) follow a nearly Gaussian distribution. Also, ln[p( J(tau) )/p(- J(tau) )] versus J(tau) can be fitted by strikingly linear functions, the slopes being proportional to tau for large tau . These results indicate that validity of the fluctuation theorem requires neither a many-particle system nor a stochastic process, which are requirements used in previous works.