Following Swendsen, we allow two systems to exchange particles.  This essentially makes room in phase space for particles to enter or leave without requiring a change in the number of dimensions of phase space.  The total number of particles is :
*  particles have coordinates .
*: The total energy of these particles is 
*  particles have coordinates .
*: The total energy of these particles is 
* The system is subject to the constraints,  and 
Taking the integral over phase space, we have:
The question marks (?) serve as a reminder that we may not assume that the first n particles (i.e. 1 through n) are in system A while the other particles (n through N) are in system B. (This is further discussed in the next section.)
Taking the logarithm and keeping only the largest terms, we have:
This can be interpreted as the sum of the entropy of system A and system B, both extensive.  And there is a term, , that is not extensive.