Table 3.

At thermal equilibrium, our numerical observations for velocity distribution and temperature of the nanoparticle along with the constraints obtained using various correlated and uncorrelated noise schemes. Abbreviations are MBD: Maxwell-Boltzmann distribution; OUP: Ornstein-Uhlenbeck process; MLN: Mittag-Leffler noise; IT: Iwashita's thermostat.

Thermostat Equilibrium
Thermostat	Velocity distribution and equipartition theorem	Constraints	Implementation remarks
White noise	Does not satisfy MBD and equipartition theorem	Δt < τb for stability	(i) Depends on position and shape of the particle, (ii) does not conform to GLE, and (iii) imbalance between memory and friction
OUP	Satisfies MBD and equipartition theorem	Δt < τb for stability; τ > τν for thermostat to work	(i) Depends on position and shape of the particle and (ii) approximately conforms to GLE
MLN	Satisfies MBD and equipartition theorem	Δt < τb for stability; τ > τν for thermostat to work; α0(λ) and β0(λ) are independent of τ in a small plateau region where τ ≳ τν	(i) Does not depend on position and shape of the particle and (ii) approximately conforms to GLE
IT	Satisfies MBD and equipartition theorem	Δt < τb for stability	(i) Does not depend on position and shape of the particle and (ii) does not conform to GLE