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

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,tau) entropy, which measures the amount of information generated by unit time at different scales tau 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 epsilon (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.