Exploring the Nosé Hoover Thermostat for MD Simulations

[SchroedingersLion]

Hi,

is anyone here familiar with the Nosé Hoover Thermostat for the realization of a canonical ensemble in a molecular dynamics simulation?

I have a few questions to the derivation and I only have the original paper of Nosé where the basics are derived. I uploaded it here: http://docdro.id/83YghJO
The section IIA.

My questions:
1) does virtual variable also imply virtual time? E.g., is the virtual coordinate q dependent on the virtual time t or can you write the virtual q both way, with virtual time t and with real time t'?

2) Is he using the new variable s with respect to virtual time t or with respect to real time t'?

3) What does q=q' mean? Does that mean that, if you insert the same virtual time t in q and q', both are identical? Or does that mean q(t)=q'(t') where t' is the point in time that corresponds to t? Or is that the same... I am confused.

In case someone knows, I would appreciate the help!

Regards

 

[lofgran]

Hello,

Thank you for your questions about the Nosé Hoover Thermostat. I am familiar with this thermostat and I will do my best to answer your questions based on my understanding.

1) In the context of the Nosé Hoover Thermostat, the virtual variable refers to the fictitious coordinate q, which is used to describe the dynamics of the system. This virtual coordinate is not dependent on time, but rather serves as a mathematical construct to help simulate the dynamics of the system. Time is still represented by the real time t' in the equations.

2) The new variable s is also with respect to real time t'. This variable is used to create a Hamiltonian for the system that includes the thermostat.

3) In this context, q=q' means that the virtual coordinate q is equivalent to the real coordinate q' at a given time t. In other words, q(t)=q'(t') where t' is the corresponding time for the virtual coordinate q.

I hope this helps clarify some of your confusion. If you have any further questions, please don't hesitate to ask. Best of luck with your research!