Abstract. In a toroidally symmetric tokamak system, total toroidal angular momentum is conserved. Total particle and total energy, i.e., a sum of total kinetic and potential energies, may also be conserved in the same time scale. At the FEC 2000 we reported that profiles of the tokamak plasmas with an internal transport barrier (ITB) are explained by the minimum (or maximum) conditions obtained by the first order variation method under the constraint of their conservation. However, the physical mechanism presented at that time was not very solid. Since then, studies on second order variations and further analysis of DIII-D and JT-60U experimental data have revealed that ITB plasmas correspond to the minimum energy state under the constraint while L-mode plasmas without ITB do not. Since the condition for the minimum energy state gives very specific relations between the density and toroidal rotation profiles, it is likely that the ITB plasmas are self-organized. This explains stiff profiles for ITB plasmas claimed in many tokamak devices. In this paper we present the theoretical conditions for the minimum energy state and the results of their tests against the actual plasmas with/without ITB.