  Dynamical systems in equilibrium have a stationary entropy; we suggest that
elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may
have a unique specific entropy. This uniqueness, a priori unknown, should be
reflected in correlations between the parameters describing the mass (light)
distribution in galaxies. Following recent photometrical work (Caon et al.
1993; Graham & Colless 1997; Prugniel & Simien 1997), we use the Sersic law to
describe the light profile of elliptical galaxies and an analytical
approximation to its three dimensional deprojection. The specific entropy is
calculated supposing that the galaxy behaves as a spherical, isotropic,
one-component system in hydrostatic equilibrium, obeying the ideal gas state
equations. We predict a relation between the 3 parameters of the Sersic,
defining a surface in the parameter space, an `Entropic Plane', by analogy with
the well-known Fundamental Plane. We have analysed elliptical galaxies in Coma
and ABCG 85 clusters and a group of galaxies (associated with NGC 4839). We
show that the galaxies in clusters follow closely a relation predicted by the
constant specific entropy hypothesis with a one-sigma dispersion of 9.5% around
the mean value of the specific entropy. Assuming that the specific entropy is
also the same for galaxies of different clusters, we are able to derive
relative distances between the studied clusters. If the errors are only due to
the determination of the specific entropy (about 10%), then the error in the
relative distance determination should be less than 20% for rich clusters. We
suggest that the unique specific entropy may provide a physical explanation for
the distance indicators based on the Sersic profile put forward by Young &
Currie (1994, 1995) and discussed by Binggeli & Jerjen (1998).
