On the two principal curvatures as possible entropic barriers in a mesoscopic nonequilibrium thermodynamics model of complex matter agglomeration

TL;DR

This paper explores how geometric curvatures, specifically Gaussian and mean curvature, act as entropic barriers in mesoscopic models of matter agglomeration, linking thermodynamics with geometric obstacles.

Contribution

It proposes geometric-kinetic obstacles as entropic barriers in matter agglomeration, highlighting the roles of Gaussian and mean curvature based on different physical potentials.

Findings

Gaussian curvature emphasizes entropic barriers with Coulomb potential

Mean curvature plays a key role with logarithmic potential

Model successfully applied to metallurgical and biophysical agglomeration

Abstract

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.