Extremum Principles in the Theory of Thermal Conductivity of a Solid

It is shown that the principle of minimum of entropy production under steady-state conditions is correct for one-dimensional geometry at arbitrary temperature dependences of thermal conductivity and specific heat in some region of values of these coefficients rather than only at a concrete dependence of thermal conductivity in the principle formulation. However, in this case, in view of the absence of a variational description, it is only possible to investigate the validity of just the necessary condition of the principle correctness. In view of this, another variational principle is suggested, which is defined as the principle of minimum algebraic sum of squares of dissipative flows and is free of the defects of the first principle.