# [lammps-users] (no subject)

Hi,
A system with constant density and temperature can be reached, if I use nve or nvt ensemble to equilibrate system.
However, what about a system with constant density, temperature, and pressure?
Temperature seems much easier to be controlled than pressure.
My question is that if I control pressure as well as temperature with a constant density, all of which should be constant in one state, the density will change somewhat due to change of volume. How can it happen?

Sincerely, yours

Email: [email protected]…8… / [email protected]…127…
Cell: 573-864-5846
Mechanical & Aerospace Engineering,
College of Engineering,
University of Missouri - Columbia

Hi,
A system with constant density and temperature can be reached, if I use nve or nvt ensemble to equilibrate system.
However, what about a system with constant density, temperature, and pressure?
Temperature seems much easier to be controlled than pressure.
My question is that if I control pressure(like, press/berendsen ) as well as temperature with a constant density, all of which should be constant in one state, the density will change somewhat due to change of volume. How can it happen?

Sincerely, yours

Email: [email protected]…8… / [email protected]…127…
Cell: 573-864-5846
Mechanical & Aerospace Engineering,
College of Engineering,
University of Missouri - Columbia

Dont you know the equation of state? Basically, temperature, volume (density) and pressure are not independent quantities. You can not “arbitrarily” control both of them all at once unless you know exactly what the values they are.

Best,

AC

2011/1/31 毛益进 <[email protected]…8…>

2011/1/31 毛益进 <[email protected]>:

Hi,
A system with constant density and temperature can be reached, if I use nve
or nvt ensemble to equilibrate system.

this has nothing to do with equilibration. if you keep the volume
(simulation box)
fixed and the number of particles constant (periodic boundary conditions), then
you automatically have a constant density.

a "constant" temperature can only be reached for an infinitely large sample,
however people often talk about "constant temperature" simulations or "nvt
ensemble", if a finite system is coupled through some algorithm to a (large)
heat bath that models the exchange of kinetic energy with the environment
of the sample that you look at.

the impact of equilibration is that your potential energy does not drift,
i.e. it keeps fluctuating around some constant value.

temperature is not that well defined for a finite sample, we usually identify
an "instantaneous temperature" by relating the total kinetic energy to
the number of degrees of freedom and the boltzman constant.
you can find more details on this subject in a book on statistical mechanics.

However, what about a system with constant density, temperature, and
pressure?

for pressure the situation is similar to temperature. we identify the
pressure of a system through an expression derived from the virial theorem
and this is implemented via fix npt.

Temperature seems much easier to be controlled than pressure.

this is due to the fact that one typically looks at systems, that
are not very compressible (dense liquids and solids).

My question is that if I control pressure as well as temperature with a
constant density, all of which should be constant in one state, the density
will change somewhat due to change of volume. How can it happen?

it cannot:

in an nvt ensemble you (try to) keep the number of particles, the volume
and the temperature constant. n and v are constant by definition, so you
only need to model the exchange of kinetic energy with the environment.

in an npt ensemble the volume is no longer constant and cannot be constant.
as a consequence, the density will fluctuate, since the number of particles n
is still constant by definition.

again, this is all explained in great detail in textbooks on
statistical mechanics,
a literature that is highly recommended to familiarize yourself with _before_

cheers,
axel.

temperature is not that well defined for a finite sample, we usually identify
an “instantaneous temperature” by relating the total kinetic energy to
the number of degrees of freedom and the boltzman constant.
you can find more details on this subject in a book on statistical mechanics.

that’s right, according to equipartition theorem.

this is due to the fact that one typically looks at systems, that
are not very compressible (dense liquids and solids).

since gases are more compressive than liquids or solids, therefore the pressure in a gases system lowly fluctuates than that in a liquids/solids system.

cheers,
christopher

Constant density means constant volume. Constant
pressure means changing the volume (to adjust the
pressure). You can't have it both ways.

Steve

2011/1/31 毛益进 <[email protected]>: