  In the present paper, we show that elliptical galaxies (Es) obey a scaling
relation between potential energy and mass. Since they are relaxed systems in a
post violent-relaxation stage, they are quasi-equilibrium gravitational systems
and therefore they also have a quasi-constant specific entropy.
  Assuming that light traces mass, these two laws imply that in the space
defined by the three S\'ersic law parameters (intensity Sigma_0, scale a and
shape nu), elliptical galaxies are distributed on two intersecting 2-manifolds:
the Entropic Surface and the Energy-Mass Surface.
  Using a sample of 132 galaxies belonging to three nearby clusters, we have
verified that ellipticals indeed follow these laws. This also implies that they
are distributed along the intersection line (the Energy-Entropy line), thus
they constitute a one-parameter family.
  These two physical laws (separately or combined), allow to find the
theoretical origin of several observed photometrical relations, such as the
correlation between absolute magnitude and effective surface brightness, and
the fact that ellipticals are located on a surface in the [log R_eff, -2.5 log
Sigma_0, log nu] space. The fact that elliptical galaxies are a one-parameter
family has important implications for cosmology and galaxy formation and
evolution models. Moreover, the Energy-Entropy line could be used as a distance
indicator.
