A skin made up by finitely many particles is a manifold passing through a finite system of interacting particles. The discrete medium as well as the continuum are characterized by the virtual work. We study equilibrium configurations of the discrete system as well as of the skin and compute the vibrational modes.\par Non-trivial equilibrium configurations only exist if the virtual work is nonlinear. Free energy, equilibrium configuration and the vibrational modes crucially depend on the structural capillarity. This sort of capillarity determines the work caused by distorting the area of the skin. The free energy of the skin is extracted from the virtual work by solving a boundary problem and is linked to a Gibbs statistics of the finite system. This yields various interplays between geometry, topology, analysis and statistics.
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