Applicability of the observable drift formalism to more complex systems

Determine how effectively the observable drift approach—based on the time-integrated deviation of an observable from its time average and the associated drift variance and diffusion exponent—classifies dynamics in more complex dynamical systems beyond the one- and two-dimensional discrete-time maps analyzed in this work, to assess its robustness and generality.

Background

The paper introduces the observable drift as a probe of chaos that generalizes the adiabatic gauge potential framework to generic classical systems. It demonstrates the method on standard testbeds (tent map, logistic map, Chirikov standard map) and links diffusion of the drift to decaying correlations and weak mixing.

While these examples support the method, the authors explicitly note that the performance and reliability of the observable drift framework in more complex settings remain uncertain, motivating systematic exploration across higher-dimensional or otherwise more intricate systems.