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Molecular dynamics (MD) often use a thermostat so that they can control the temperature. Temperature tends to drift due to endo/exothermic reactions (that would normally absorb/emit heat to a large thermal bath) and numerical errors.

Thermostats are a bit cumbersome, each has significant disadvantages (i.e. "flying ice cube" effect). How about a thermostat that simply sets a global damping coefficient on the short-range interactions? If we are too cold, it would set a negative damping to add energy and warm us up, and visa-versia if we are too hot. This would inject or remove energy mostly from the higher frequency vibrations, which is where numerical error tends to originate. This idea seems good at first glance, but it must have important issues of it's own. What are the problems with using this thermostat, and does this thermostat have a name in the literature?

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I suspect that it is hard to do what you propose: MD simulations are for the purpose of seeing how the small scale physics affects the large scale physics. Mucking around with the small scale physics to achieve thermalization will make it difficult to draw conclusions. However, I'm not up to date on the state of the art in this area. –  Dave Oct 29 '13 at 18:03
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You are looking for something called Nose-Hoover thermostat. It precisely does what you are saying. It sets a damping coefficient and a set temperature. The damping is proportional to the difference in the present temperature and set temperature. It is highly robust compared to the velocity rescaling according to the temperatures which could lead to flying ice cube effect. There are tons of literature on Nose-Hoover thermostat. You can look for Nose-Hoover 1984 for this

There is something else called DPD thermostat which employs a thermostat which works on the principle of Dissipative Particle Dynamics. You can look into the paper Warren and Groot 1997 Disspiative particle dynamics for this.

There is Anderson thermostat as well. I am not much familiar with this. But as far as i know it tries to equilibrate by sampling velocities from a Gaussian distribution whenever temperature exceeds the set temperature

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But why do they have "fictiotous mass" and "ficticous degrees of freedom"? That makes it sound much, much more complicated than simply a damping parameter. –  Kevin Kostlan Nov 11 '13 at 2:35
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The additional degrees of freedom are needed to blow up the system so that heat can be exchanged between the actual system variables and the additional ones in a deterministic (!) fashion. An advantage of this thermostat is that (if necessary, extended by several so-called "Nose-Hoover chains" - additional variables thermostat other additional variables) it maintains the canonical ensemble, which other velocity rescaling techniques (e.g. Berendsen thermostat) don't. I could image that the thermostat you propose suffers from the same problem. –  Simeon Carstens Nov 11 '13 at 8:15
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As for the Andersen thermostat, let me correct the this answer: in each time step, particles are chosen randomly and the velocities of these particles are redrawn from the the target Maxwell distribution. Whether velocities get updated or not is independent of the current temperature. –  Simeon Carstens Nov 11 '13 at 8:39
    
@SimeonCarstens thanks for correcting the concept about Anderson thermostat –  Vaidyanathan Nov 11 '13 at 14:02
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