Quantitative measure of memory loss in complex spatiotemporal systems

Area of Science:

• Complex Systems Dynamics
• Statistical Mechanics
• Materials Science

Background:

• Forecasting complex system evolution relies on understanding history dependence.
• Prediction accuracy degrades as system memory is lost over time.

Purpose of the Study:

• To propose a novel method for quantifying the rate of memory loss in complex systems.
• To establish a link between memory loss rate and the predictability of system states.

Main Methods:

• Developed a method applicable to experimental data in any metric space.
• Analyzed memory loss in slowly sheared granular systems with a small inertial number (I).
• Investigated the relationship between memory loss rate, shear rate, force network transitions, and shear stress correlations.

Main Results:

• The proposed method provides an upper bound on the system's mixing rate.
• Memory loss rate in sheared granular systems shows erratic dependence on shear rate, with observed bifurcations.
• A strong correlation was found between memory loss rate, force network dynamics, and macroscopic shear stress behavior.

Conclusions:

• The developed method effectively quantifies memory loss and its impact on predictability.
• Granular systems exhibit complex memory loss dynamics influenced by shear rate and internal force network evolution.
• This work bridges the understanding of micro-scale force network changes and macro-scale system properties.