Onsager’s [1,2] and Prigogine’s [3,4] type minimum principles can be treated for irreversible processes in the frame of classical irreversible thermodynamics (CIT). Results agree with Gyarmati’s [5] integral principle. It is especially worthy to investigate the irreversible heat conduction process for the case of a stationary state for which new quasilinear elliptic type PDEs derived from the principles of minimal energy dissipation and minimum entropy production. Evaluating these PDEs through the aid of the Dirichlet Integral Principle yields the first, second and third type boundary condition solutions for each minimum principle. Here the interpretation of the Dirichlet Integral Principle essentially differs from the usually known “conservative” type approach using Laplace’s equation in conjunction with potential theory. Dissipation potentials of Rayleigh and Onsager type also agree with stated results. The evolution of the process towards a stationary state can be explained with the Glanssdorff‐Prigogine criterion. Boundary conditions of thefourth kinddefine the process of conduction between a single body, or system of bodies and their surroundings. The bodies are assumed to be in perfect contact where and when the surfaces in contact have the same temperature. © 2003 American Institute of Physics