  A numerical simulation shows that the osmotic pressure of compressed lattice
knots is a function of knot type, and so of entanglements. The osmotic pressure
for the unknot goes through a negative minimum at low concentrations, but in
the case of non-trivial knot types $3_1$ and $4_1$ it is negative for low
concentrations. At high concentrations the osmotic pressure is divergent, as
predicted by Flory-Huggins theory. The numerical results show that each knot
type has an equilibrium length where the osmotic pressure for monomers to
migrate into or our of the lattice knot is zero. Moreover, the lattice unknot
is found to have two equilibria, one unstable, and one stable, whereas the
lattice knots of type $3_1$ and $4_1$ have one stable equilibrium each.
