Quantum mechanical aspects of order evolution processes – the case of nanoporous aluminum oxide

Porous ordered anodic alumina (PAOX) is a textbook example of macroscopic self-organization. It is often regarded as a blueprint of a dissipative structure, characterized by its highly ordered pore appearance formed by electrohydrodynamic processes and related flow cells. Considering the pores and flow cells, our findings reveal for the first time that the collective development of these macroscopic bodies into hexagonal arrangements follows quantum mechanical rules. The extremal principles and laws which govern the arrangement symmetry are herein conceptually connected to eigenenergies, eigenenergy-spectra and properties of fermionic particles, and hence they form a discrete entropy production spectrum which encodes the distribution of coordination environments. These quantum mechanical aspects are embedded into a model of PAOX order evolution based on entropy production and the theory of dissipative structures.