ON THE PRINCIPLE OF MINIMUM ENTROPY PRODUCTION IN QUASILINEAR CASE AND ITS CONNECTION TO STATISTICAL MECHANICS

Abstract

Studying heat conduction problems in linear and quasilinear ranges for stationary state one can be convinced that the principle of minimum entropy production is valid, but only under special conditions. By using variational calculus we show that the solution of the minimum principle accords totally with that of the energy balance equation for both cases. Of course, the Euler-Lagrange differential equations for linear and quasililnear cases do not give the same solutions and similarl, the temperature distributions differ, too. Nevertheless, according to a deeper analysis we can suspect that only non linear heat conduction exists. Investigations from the point of view of the picture representation and a special new method developed for the solution of the variational problem refer to this. The empirical Fourier's law does not seem to fit the energy balance equation because this linear process does not appear exactly in this form in nature. The formal proof for Fourier's law with the energy balance equation very probably is delusive.