Unified description of thermal behaviors by macroscopic growth laws

Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. The known classification schemes of the growth laws refer to time evolution of biological and technical systems. We propose to apply the previous classifications to phenomenological analysis of thermal systems with a cross-fertilization among different sectors. As an example, the Fermi-Dirac distribution function and the electrical activation in implanted silicon carbide are discussed.