Re: How to calculate entropy of particles?

Rick Giuly wrote:
On Feb 14, 11:40 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:
On Feb 14, 9:22 pm, Rick Giuly <rgiuly.gr...@xxxxxxxxx> wrote:

Hello all,
I'm working on a molecular dynamics simulation based on Lennard-Jones
potential. Each particle has a position, a mass, and a velocity.
I know that temperature is the average kinetic energy of all the
particles, so temperature is no problem to calculate.
But, how would you calculate the entropy of the particles?
S = k ln(number of states)
dS = dQ / T



Any help is appreciated.
-Rick Giuly
If replying by email please use: rgiuly at ucsd dot edu
reference:http://en.wikipedia.org/wiki/Lennard-Jones_potential

The problem I have with S = k ln(number of states) is that it seems
like the number of states is nearly infinite, since there are multiple
particles and each can be at any location in space.

You are correct, your entropy is going to be infinite if you consider only classical mechanics, because number of states is infinite. What makes entropy of a real system of particles non-infinite is the quantization of the phase space of impulses according to quantum mechanics.

Calculation of entropy of ideal gases (basically billiard balls) using quantization of phase space have been done by Zakura and Tetrode, and it coincides well with experimentally measured values of entropy of noble
gases.

Zakura-Tetrode equation for entropy looks like this:

S = R*ln(2*pi*k)^3/2 / (h^3*Na*5/2) + 3/2*R*ln(M) + 5/2*R + R*ln%+5/2R*ln(T) -R*ln(p).

R is Ridberg constant, k is Bolzman constant and Na is avogadro
number. M is number of moles of gas, and p is pressure.

Note that formula includes Plank constant h, which makes very clear
quantum mechanical nature of "finite" entropy.

The only source for this derivation that I could find in in russian
book "course of physical chemistry", band I, by Gerasimov.

But similar discussion of entropy derivation is given here:
http://physics.nmt.edu/~raymond/classes/ph13xbook/node241.html

Regards,
Evgenij





dS = dQ / T
This formula tells me something about how the entropy would change
when heat is added but I want to calculate the entropy as a function
of the position and velocity of all the particles at an instant in
time.

So I'm still not sure how to calculate the entropy (as a function of
the position and velocity of all the particles at an instant in time).

-Rick
.

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