TABLE 3.

Comparion between the numerically predicted results by FHD and GLD with MLN methods. Abbreviations, EQT: Equipartition theorem; VACF: Velocity autocorrelation function; MSD: Mean square displacement.

Comparison: FHD & GLD with MLN
EQT	FHD: Equipartition theorem is satisfied. The particle mass m is augmented by an added mass m0/2, to account for compressibility.
	GLD: Equipartition theorem is satisfied. When the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel.
VACF	FHD: The translational and rotational VACFs of the particle follow an exponential decay, exp(−ζ(t)t/M) and exp(−ζ(r)t/I)), respectively, at short times, and a power-law decay, a0 (t/τν)−3/2 and b0 (t/τν)−5/2, respectively at long times. The value of a0 and b0 agrees with Hauge and Martin-Löf [10].
	GLD: The translational and rotational VACFs of the particle follow a stretched exponential decay, exp{−(t/τν)3/2}, at short times, and a power-law decay, a0 (t/τν)−3/2 and b0 (t/τν)−5/2, respectively, at long times. The value of a0 and b0 differs from those predicted by Hauge and Martin-Löf [10].
MSD	FHD: In the diffusive regime, translational and rotational MSDs obey Stokes-Einstein and Stokes-Einstein-Debye relations, respectively.
	GLD: In the diffusive regime, translational and rotational MSDs obey Stokes-Einstein and Stokes-Einstein-Debye relations, with scaling factors of 3 and 102.54, respectively.