Isodynamic and Equilibrium Processes

There is a striking difference between an equilibrium process and a process that runs at constant energy. Both for an isodynamic process and for an equilibrium process in an isolated system dt/=0. If the energy is a function of a set of variable Xi, X2,U= U X, X2.). then these variables may change in some way that the energy remains constant U = C, then the condition dC/ = 0 is certainly fulfilled. This is tme for an isodynamic process and for an equilibrium process. We emphasize that an isodynamic process is not necessarily an equilibrium process. 

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We are dealing here with an isodynamic process, but not with an equilibrium process. Further, since we do not allow the exchange of matter, the mol numbers and thus the corresponding chemical potentials are not relevant in the present consideration. 

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