On page 014101-3, the Bussi paper (http://dx.doi.org/10.1063/1.2408420)
mentioned: "On the other hand, for coupling constant approaching
infinity,the Hamiltonian dynamics is recovered."
Does that means that for a large enough coupling constant, the velocities
are nearly not rescaled, and the dynamics (like rate of motion) would be
same as that of NVE?

A larger coupling constant, means a smaller diffusion coefficient in the
axillary dynamics by equation 6.

While the effects of the velocity rescaling at each step will accumulate, a
larger coupling constant means the thermostat perturb less of the dynamics,
and the resulting dynamics is closer to a NVE simulation.
There is no worry that the thermostat would suddenly rescale the dynamics
every x step, because in the procedure of the thermostat, the velocities
are rescaled every step, regardless of the coupling constant.

I guess, if I pick a coupling constant that is just small enough to keep
the energy conserved, I would get a NVT simulation that is as close as a
NVE simulation as possible.

Is this correct?
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