  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 Fokker-Planck
type. One of central problems arising when applying it to the matter
agglomeration phenomena, quite generally termed nucleation-and-growth process,
appears to be some physically accepted identification of entropic barriers, or
factors impeding growth. In this paper, we wish to propose certain
geometric-kinetic obstacles as serious candidates for the so-called entropic
barriers. Within the framework of the thermodynamic formalism offered they are
always associated with a suitable choice of a physical potential governing the
system. It turns out that a certain choice of the potential of Coulomb (or,
gravitational) type leads to emphasizing the role of the Gaussian curvature
while another choice in a form of the logaritmic physical potential results
unavoidably in a pronounced role of the mean curvature. The whole reasoning has
been tested succesfully on a statistical-mechanical polycris- talline evolution
model introduced some years ago for physical-metalurgical purposes, and
modified for a use in biophysical soft-matter agglomerations.
