Origin of the scaling rule for fundamental living organisms based on thermodynamics

The regular relationships between metabolic energy and body mass M of unicellular organisms, poikilotherms and homeotherms were well known as general equations. The metabolic energy rate and the life span are proportional to M0.75 and to M0.25, respectively. As a result, the product of the metabolic energy rate and the life time, namely, life metabolic energy, is proportional to the mass of the living organism. The origin of the scaling rules for environmental organizing systems is as follows: (1) the scaling rules for internal energy, activation energy and free energy as a function of temperature and mass of a mole of molecules. (2) The majority of species of the living organisms have the same molecules such as polysaccharides, lipids, proteins and nucleic acids in nearly same the ratio. (3) The internal energy of reactants in living organisms is equilibrium with the internal energy of water. Then, the integrated metabolic energy over the synthesizing time depends on internal energy of water and is proportional to mass M, despite the synthesizing time of the system depending on reaction rate. The proportional constant is obtained based on the thermodynamics for fundamental living organisms such as unicellular organisms and plants. Information on the environmental organizing system is also discussed.