Further remarks on the second law of thermodynamics in general relativity

In a previous article(1) I have attempted an extension of thermodynamics to general relativity, and in following articles(2) have discussed certain applications of this extension. The postulate that was taken in this work as the analogue of the ordinary first law of thermodynamics was the same as the modified principle of the conservation of energy given by Einstein(3) as applying in the case of general relativity considerations.