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In the present paper, we show that elliptical galaxies (Es) obey a scalingrelation between potential energy and mass. Since they are relaxed systems in apost violent-relaxation stage, they are quasi-equilibrium gravitational systemsand therefore they also have a quasi-constant specific entropy.  Assuming that light traces mass, these two laws imply that in the spacedefined by the three S\'ersic law parameters (intensity Sigma_0, scale a andshape 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 haveverified that ellipticals indeed follow these laws. This also implies that theyare distributed along the intersection line (the Energy-Entropy line), thusthey constitute a one-parameter family.  These two physical laws (separately or combined), allow to find thetheoretical origin of several observed photometrical relations, such as thecorrelation between absolute magnitude and effective surface brightness, andthe fact that ellipticals are located on a surface in the [log R_eff, -2.5 logSigma_0, log nu] space. The fact that elliptical galaxies are a one-parameterfamily has important implications for cosmology and galaxy formation andevolution models. Moreover, the Energy-Entropy line could be used as a distanceindicator.Comment: Revised version (considering non constant M/L), accepted by A&A on  10/03/0

Energy, entropy and mass scaling relations for elliptical galaxies. Towards a physical understanding of their photometric properties