# [gmx-users] RE: Isobaric - isothermal ensemble and Replica Exchange

X.Periole X.Periole at rug.nl
Wed Nov 16 22:16:54 CET 2005

```Hello Luca,

> In an NPT simulation is the exchange probability among
>replicas the same
> as in NVT or does it change ? In my simulation I have 46
>replica NOT
> equally spaced (from 1K to 3 K), every couple of replica
>exchanges
> actually, but the probability of mine has the shape of a
>decreasing
> exponential, and the real question is: is it normal or
>dos it have to be
> similar to that of a canonical REMD with all the
>probabilities falling in
> the same range of values ?

The probability of exchange or the observed exchange ratio
between to consecutive replicas is completely and only
determined by their respective distribution of potential
energies. That is for the NVT case. In the NPT case there
is the Pv term that will correct the Epot but already said
it is samll.
If you do not have a constant acceptance ratio that means
that your temperatures are not distributed correctly. A
decreasing exponential would indicate that when your
temperature increases yhe interval between them is get too
large.

In principle I don't see any reason for the acceptance
ratio to be constant, beside the fact that you would not
have the same residence time at each temperature. Of
course the acceptance ratio (mixed with the interval
between two
exchange trials) must let your system enought time to
explore the new potential surface to loose the memory of
the previous one. In this case the thermodynamic ensemble
is still correct, but comparing the different temperature
is dangerous because you do not know the bias introduced
by switching the temperature of your system all the time.
So
better doing it in a similar way over the range of
temperatures.

>
> If my exchange probability is fine, then, I van compute
>thermodynamic
> quantities ... but if it's failed I have to understang
>exactly what's
> going on .....
>
>isobaric -
> isothermal ensamble, I would be interested in the
>treatment of the theory
> and the statistical mechanics of the problem, but
>unfortunately the
> treniest treatement is the one of canonical
>distributions ... do you have
> any suggestions regardin bibliography ?

Look for simulated tempering ?! temperature walk ?!

Best
XAvier

```