A contribution to extended irreversible thermodynamics

Concepts of extended irreversible thermodynamics (EIT) are explored for continuous systems away from equilibrium. The principle of the minimum entropy production is studied to find a possible generalization to the EIT region. Onsager - Machlupʹs theory is reformulated for continuous systems. The emphasis of this study is placed on the role of the extended Gibbs relation for the entropy differential. It is found that the nonequilibrium entropy, whose differential is never exact, relaxes to the extended entropy, for which we presume the extended Gibbs relation to give the thermodynamical meaning to the intensive thermodynamic variables.