On the two principal curvatures as potential barriers in a model of complex matter agglomeration

We show that matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the well-known flux-force relations, with the Onsager coefficients involved, ending eventually up at a local conservation law of the Fokker-Planck type. Within the framework of the formalism offered the first two curvatures, characterizing the structure of the agglomerates, are associated with a suitable choice of a physical potential governing the system. It turns out that a certain choice of the potential of power-law type leads to emphasizing the role of the Gaussian curvature while another choice in logarithmic form results in a pronounced role of the mean curvature. The offered modeling has been related successfully with a statistical-mechanical polycrystalline matter evolution introduced for physical-metallurgical purposes, and modified for a use in biophysical soft-matter agglomerations