Universal size/shape-dependent law for characteristic temperatures

The description of different effects observed in nature by only one general equation is the “Holy Grail” for all physicists. This goal has been achieved for characteristic temperatures through a top-down approach and is presented here. The general equation is based only on the surface area to volume ratio of nanostructures and statistics (Fermi–Dirac or Bose–Einstein) followed by the particles involved in the considered phenomena (melting, ferromagnetism, vibration and superconduction). From the distinction between fermions and bosons, this equation indicates the universal behaviour of size and shape effects. Theoretical predictions show satisfactory agreement with experimental data taken from literature.