In the absence of external work, and heat transfer, the total energy of a system (mechanical + thermal) will remain constant. Such a system is commonly referred to as isolated.
Internal conservative forces cannot change the total energy of a system by definition, since the work they do is encapsulated by internal potential energy terms. However, we cannot treat internal non-conservative forces as easily. Though it is clear that for the total energy of the system to be conserved, the total work done by all internal non-conservative forces must be zero.
Is there a way of proving mathematically that this is so, perhaps in the case of a system containing multiple interacting particles? Evidently, internal non-conservative forces can each do non-zero work, and can change the relative amounts of different forms of energy in the system, but they cannot change the total amount.
I wondered whether anyone could help!