Interplay between geometry and thermodynamics: the morphometric approach

The fluid density distribution close to a complexly shaped object and corresponding thermodynamic quantities, such as the solvation free energy of that object, are computational expensive due to the lack of spatial symmetry. The morphometric approach presented in this talk is based on the Hadwiger theorem from integral geometry. It proposes a complete separation of the grand potential of the system into geometrical measures, characterizing the complex geometry, and corresponding thermodynamic coefficients, describing the fluid and the wall-fluid interaction. We employ a combination of density functional theory of classical fluids and exact statistical mechanical sum-rules to substantiate the approach.

The complete separation of the grand potential into geometrical measures and thermodynamic coefficients is a generalization of the concept of extensivity and allows one to transfer experience from simple to complex geometries. We introduce the morphometric approach and discuss its application to the calculation of the solvation free energy of proteins.