Probing intrinsic noise correlation time in non-Markovian diffusive systems

The generalized Langevin equation describes molecular motion in complex systems using memory and random noise terms. Memory effects, the inherent time correlation in random noise, significantly influence molecular diffusive behaviors. However, estimating the intrinsic noise correlation time remains challenging because of difficulties in measuring the memory term. We propose a metric to probe the noise correlation time based on the deviation between characteristic times of configurational diffusion and "diffusion motion" in the kinetic energy space. This approach stems from the observation that memory effects delay relaxation time between displacement and velocity response functions. Our metric relies solely on the velocity autocorrelation function, commonly used in experimental model parameterization. Both analytical and numerical results for various physical models demonstrate its effectiveness in probing noise correlation time. Furthermore, we apply this metric to study complex diffusive phenomena, including non-exponential relaxation in molecular hydrodynamics and anomalous diffusion in crowded environments. By comparing with system's relaxation time, we reveal that long-range noise correlations play a key role in these non-trivial diffusive phenomena.