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On the problem of the minimum entropy production in the nonequilibrium stationary state

“…) which coincides with (3.17) in the adopted approximation. The obtained results generally support the conclusions under p 3.1 (see also [12][13][14][15]). A question arises as to the existence of the inverse statement 8 , that is, if the stationary field of temperatures provides, at least roughly, the minimum entropy production.…”

“…Considering the recent interest aroused in the applicability of the minimum principle at the power dependence of the thermal conductivity coefficient on the temperature [14,15], we shall assume…”

“…The great interest attached to the principle can be explained by the apparent intuitive simplicity and universality of the proposed statement. This factor just led (and still leads) to numerous misbelieves on this theorem (see, for example, [11][12][13][14][15][16][17]20]). As a result, two essentially extreme opinions have been formed in the literature.…”

Irreversibility and Action of the Heat Conduction Process

“…For the heat conduction process, the least action principle can be used to derive Fourier's heat conduction law, and then to optimize heat transfer problems. Several works [17,25,26] related to the least action principles of the heat conduction process have been published. Here, we will give a brief review of this topic to highlight that the action of the heat conduction process is unique, which is associated with the entransy dissipation rate, rather than the entropy production rate.…”

“…For example, entransy [15,16] and its dissipation rate can also serve as Lyapunov functions for heat conduction processes in order to reflect the processes' irreversibility. The emergence of entransy theory is due to the deficiency of the entropy production rate in handling heat conduction problems [17][18][19][20]. Although the entransy theory has been proven to be efficient for handling the heat transfer problems [16], a rigorous proof is still needed to clarify that the entransy and its dissipation rate are indeed associated with the irreversibility of the heat conduction process.…”