Table 1.

A summary of comparison of equilibrium properties between the hybrid (current), fluctuating hydrodynamics, and generalized Langevin approaches. Abbreviations, MBD: Maxwell-Boltzmann distribution.

Method	Equipartition	Remarks
Hybrid	Satisfies MBD and equipartition theorem	Δt < τb for stability; thermostat works in a plateau region in the (τ1/τν), (τ2/τν) plane
Fluctuating hydrodynamics [22]	Satisfies MBD and equipartition theorem only with an added (virtual) mass correction	Δt < τb for stability; compressibility effects are accounted by adding the virtual mass with the particle mass
Generalized Langevin dynamics [30]	Satisfies MBD and equipartition theorem	Δt < τb for stability; τ > τν for thermostat to work and satisfies equipartition theorem in a small plateau region where τ ≳ τν