A note on maxima and minima of dissipation in context of treatment of irreversible thermodynamic systems by application of Extremal Principles

It is generally accepted that the kinetics of evolution of dissipative systems (e.g. by diffusion) can be treated by Extremal Principles. There is still quite a confusion concerning which extremum (maximum or minimum) of the dissipation corresponds to the system evolution. In the paper it is clearly shown that if the system is in general non-equilibrium state its evolution corresponds to the instantaneous constrained maximum of dissipation. In contrary, if the system reaches its steady state, the dissipation is minimized with respect of all possible ways of system evolution consistent with fixed conditions on its surface. Moreover, the value of the maximal dissipation in most cases decreases to its minimum value when the actual configuration approaches its steady state. Although the results show agreement with the existing literature, the problem is still not sufficiently clarified there.