A note concerning some aspects for application of a thermodynamic extremal principle (TEP) for continua

A matter of fact is that extremal principles have been introduced in mechanics in more (Euler, Lagrange) or less (Hamilton) than 200 years ago. One may also observe an impact of thermodynamic extremal principles based on maximum dissipation due to all the entropy production expressed in several disciplines. According fields are theory of communication, statistical mechanics and later physics of earth since already 70 years. The current paper offers some (historical) overview on several applications. “Ziegler’s principle” is an implementation of the maximum entropy production going out to the dissipation and yielding a maximum dissipation. The goal of this paper is now the implementation of this extremal principle performed along an algebraic concept. Such a concept can be extended to a system with several internal variables as outlined by Coleman and Gurtin in context with the Gibbs (free) energy.v