Table 4.

Our numerical observations for VACF and MSD of the nanoparticle obtained using various correlated noise schemes. Abbreviations are OUP: Ornstein-Uhlenbeck process; MLN: Mittag-Leffler noise; IT: Iwashita's thermostat.

Thermostat Dynamics
Thermostat	VACF	Diffusivity	Remarks
OUP	Follows an exponential decay at short and long times	Not considered in this study
MLN	Follows (i) an exponential decay at short times and (ii) an algebraic decay over long times (translational: t−3/2 and rotational: t−5/2)	Obeys Stokes-Einstein (translation) and Stokes-Einstein-Debye (rotation) relations, with scaling factors of 12 and 103.2, respectively	Conformed to hydrodynamic wall interactions
IT	Follows (i) an exponential decay at short times and (ii) an algebraic decay over long times (translational: t−3/2 and rotational: t−5/2)	Not considered in this study