Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time-series analysis

The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Results obtained in a previous work [M. Romero-Bastida, Phys. Rev. E 69, 056204 (2004)] suggest that the impurity does not contribute significantly to the dynamics of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. The (r, τ) entropy, which measures the amount of information generated by unit time at different scales τ of time and r of the observable, is numerically computed by methods of nonlinear time-series analysis using the position and momentum signals of the heavy impurity for various values of the energy density ∈ (energy per degree of freedom) of the system and some values of the impurity mass M. Results obtained from these two time series are compared and discussed.