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The problem of detecting specific features of microscopic dynamics in themacroscopic behavior of a many-degrees-of-freedom system is investigated byanalyzing the position and momentum time series of a heavy impurity embedded ina chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Resultsobtained in a previous work [M. Romero-Bastida, Phys. Rev. E {\bf69}, 056204(2004)] suggest that the impurity does not contribute significantly to thedynamics of the chain and can be considered as a probe for the dynamics of thesystem to which the impurity is coupled. The ($r,\tau$) entropy, which measuresthe amount of information generated by unit time at different scales $\tau$ oftime and $r$ of the observable, is numerically computed by methods of nonlineartime-series analysis using the position and momentum signals of the heavyimpurity for various values of the energy density $\epsilon$ (energy per degreeof freedom) of the system and some values of the impurity mass $M$. Resultsobtained from these two time series are compared and discussed.Comment: 7 pages, 5 figures, RevTeX4 PRE format; to be published in Phys. Rev.

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