# Difference between two approaches for calculating density evolution with temperature

Dear all,

I’m studying how cooling a polymer from 300K to 100K affects its density and I would like to ask you which is the difference between these two approaches:

Option 1)

Fix 1 npt temp 300 100 10 1 1 20

Run 10000

#And taking as density the one of each time step (thermo_style custom density)

Option 2)

Fix 1 npt temp 300 300 10 1 1 20

Run 10000

Unfix 1

#Take as density the mean once it reaches equilibrium

Fix 1 npt temp 275 275 10 1 1 20

Run 10000

Unfix 1

#Take as density the mean once it reaches equilibrium

Fix 1 npt temp 275 250 10 1 1 20

Run 10000

Unfix 1

#Take as density the mean once it reaches equilibrium

Fix 1 npt temp 125 100 10 1 1 20

Run 10000

Unfix 1

#Take as density the mean once it reaches equilibrium

I think that with option 1 the values of density obtained are not valid since the equilibrium is not reached in each timestep.

Dear all,

I’m studying how cooling a polymer from 300K to 100K affects its density and
I would like to ask you which is the difference between these two
approaches:

the most obvious difference is the vastly different cooling rate.

axel.

Dear Axel,

the cooling rate is one point, indeed.

But, on the other hand, am I right when I say that with the option 1 (Fix 1 npt temp 300 100 10 1 1 20) the density I obtain at each timestep is not a correct value since it is a density obtained from a not equilibrated system?

Dear Axel,

the cooling rate is one point, indeed.

But, on the other hand, am I right when I say that with the option 1 (Fix 1
npt temp 300 100 10 1 1 20) the density I obtain at each timestep is not a
correct value since it is a density obtained from a not equilibrated system?

this is something you cannot say in all generality; there are multiple
factors at play here.

for a suitable choice of parameters, the state of the system will
remain so close to equilibrium for the individual temperature, that
you cannot tell the difference.

but there is also the question of activated processes and phase
transitions. those may or may not happen with either approach and may
require multiple decorrelated runs or bigger systems or longer
equilibration (remember, when observables don't change, this is no
proof of equilibrium, only a requirement. you could also be in a
metastable state, and it may take a very long time to drop out of it).

axel.

Dear all,

please find attached the comparison of results between option 1 (purple cross) and option 2 (red squares).

As you can see, the purple results oscilate continuously. The red points are, at the end, the mean between a lot of oscillations in a given temperature.

I consider the option 2 approach a much better approach since each point is a mean of the oscillation at this temperature.

Hmmm… That is not a fair comparison in several ways:

1. The total lengths of simulation time are different.

2. Hence the cooling rates are different

3. Purple crosses seem to be instantaneous values while the red squares are averaged values.

If you eliminate all of the above variables and have only one control variable (different heating options) then you can be more affirmative.