This commentary tackles the subtle at-the-edge problem of passing locally by a mesoscopic matter-aggregating system from a classical stochastic to a quantum stochastic description. A d-dimensional entropy-productive aggregation of the matter is taken as the starting point. Then, a dimensional reduction towards a one-dimensional quantum-wire type matter-aggregation system is proposed, resulting in postponing surface-tension conditions for the effectively d = 1-dimensional quantum-wire type or nanorod-like cluster/polycrystal, which is qualitatively consistent with a physical-metallurgical (high-temperature) Louat's grain growth model. A certain recuperative interplay based on maneuvering between subtle temperature rises applied to the system under study while maintaining its quantum character (the so-called Nelson's quantum-stochastic procedure) within the limits of a vanishing Planck's constant, involved in the diffusivity measure of the aggregation, is discussed. Certain applications towards the formation of d = 1-dimensional semiconductors and other nanostructures (possibly using soft materials or (bio)polymeric materials such as nanofibers) are envisioned. As a special example, one may propose a nanotechnological process which is termed the Van der Waals heteroepitaxy. The process itself contains the main quantum vs. classical crossover due to the involvement of weak repulsion (quantum) vs. attraction (treated classically) interactions, which are represented by a Lennard-Jones-type potential.
Keywords: Fokker–Planck type equation; entropy production; nanostructure formation; nonequilibrium mesoscopic thermodynamics; quantum vs. classical; recuperation; reduction of system’s dimensionality; stochastic quantization; weak Van der Waals interaction.