Seeking advice on temp control method

Dear Lammps Users and Developers,

I am writing to seek your advice in a procedure that I used to control the system temperature, as I am not sure if this is an appropriate way to go.

I am interested in a non-equilibrium particulate suspension system. As much as I want to control the temperature but meanwhile to preserve the hydrodynamic interaction between solvent particles, I adopted DPD/tstat with a friction coefficient at 5.0; compute temp/deform has been invoked to deduct the streaming velocity that is applied to the system by fix deform, and the current erate is at 0.05; the integrator for solvent particles is fix nve. (Since I am debugging this issue, so far I am operating just in pure solvent system, with particle number at ~0.6 million)

Here is the details for the commands:
fix shear all deform 1 xy erate 0.05 remap v

compute stream all temp/deform

pair_style hybrid/overlay lj/cut 3.0 dpd/tstat 0.5 0.5 3.0 48274

pair_coeff * * dpd/tstat 5.0

* C_stream on average is about 2.3, and the system temp by default calculating by lammps is about 0.9.

Since earlier, I have found that the temperature cannot be easily controlled at all just by compute temp/deform + dpd/tstat, hence to keep the desired temperature, I added one more fix in addition to DPD/tstat: fix temp/rescale on solvent particle, which forces the temperature to be my targeting temperature. And now the temperature is controlled but the same time another concern is aroused.

The command is like this now.
fix shear all deform 1 xy erate 0.05 remap v

fix 3 all temp/rescale 1 0.5 0.5 0.01 1.0

fix_modify 3 temp stream

pair_style hybrid/overlay lj/cut 3.0 dpd/tstat 0.5 0.5 3.0 482748

pair_coeff 1 1 lj/cut 1.0 1.0 3.0

pair_coeff * * dpd/tstat 5.0

Now the c_stream is at 0.5, as it is supposed to be…
However, I am concerned it will cause some unphysical behavior. I performed some simple tests on pure solvent system, one with DPD/tstat, and the other without DPD/tstat but with fix temp/rescale, and the two system is integrated by NVE. I see a difference in diffusivity, as I assumed.

Hope to hear back your perspectives.Thanks a lot in advance.

You're using two thermostats together which is not a good idea.
The most important thing to realize is that you (presumably) want
to thermostat only the thermal part of the shear flow. There
are many ways to do that:

use compute temp/deform as a bias on any thermostat (fix nvt, fix
langevin, fix temp/rescale)
use fix langevin on the non-shearing dimensions of the flow

You could try pair dpd/tstat as a thermostat but it's not
clear to me it will work (it knows nothing about the shear flow),
and I don't see why it would be superior to any other thermostat.