To calculate the entropy of a two dimensional hard disk gas, one can begin with the partition function[9]:

where, are the position vectors and are the momentum vectors. This reduces to

This needs to be divided by *N*! because the demon does not distinguish
individual molecules, so

In terms of the partition, the entropy is

For a 2 dimensional gas,

Solving for the entropy, we get

Using Sterling's approximation for *N*!, we get

All quantities here are either known or arbitrary constants.

Mon Jun 16 13:53:44 EDT 1997