General Differential Contact Identities for Macromolecules

We discuss general Maxwell identities relating a macromolecule's charge, the forces acting at its surface, and the osmotic pressure of the solution in which it sits. The identities are closely related to the contact value relations that hold for certain special geometries, but are more general. In particular, the Maxwell identities can be applied to any macromolecule geometry, and they hold both within and outside of mean-field theory. Examples illustrate that combining the identities with approximate treatments of screening can often return simple, accurate osmotic pressure estimates.