31c) Secondly, I am examining the same but environmentally insulated mixture. The temperature change is then related to changes in its energy derived from Eq. 24c (Eq. 32a). Through taking the time derivative of 𝕊 𝑠𝑦𝑠 , using the introduced parameter 𝛼, and postulating that the heat capacities stay constant for sufficiently small temperature changes (Eq. 32b), I obtain Eq. 32c. As the term on the right side of the equation must again always be positive, I find that the total entropy must increase with time for a system that is not in equilibrium (32d