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The process of ATP production is one of the most vital processes in living cells which happens with a high e ciency. Thermodynamic evaluation of this process and the factors involved in oxidative phosphorylation can provide a valuable guide for increasing the energy production e ciency in research and industry. Although energy transduction has been studied qualitatively in several researches, there are only few brief reviews based on mathematical models on this subject. In our previous work, we suggested a mathematical model for ATP production based on non-equilibrium thermodynamic principles. In the present study, based on the new discoveries on the respiratory chain of animal mitochondria, Golfar's model has been used to generate improved results for the e ciency of oxidative phosphorylation and the rate of energy loss. The results calculated from the modi ed coe cients for the proton pumps of the respiratory chain enzymes are closer to the experimental results and validate the model.

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