On extended thermodynamics of discrete systems

Work-, heat- and material-exchange between a discrete system and its environment are derived by field-theoretical methods and can be represented by Pfaffians. The work-exchange includes the volume work as well as the deformation work. The state space of these discrete systems in nonequilibrium contains the heat exchange in addition to the time rates of the equilibrium variables, thus inducing the notation “extended” thermodynamics. The dissipation inequality is not exploited by constitutive ansatzes as usual in irreversible thermodynamics, but by Liuʹs procedure which considers all materials compatible with the chosen nonequilibrium state space. The nonequilibrium entropy does not depend on time rates and on the heat-exchange, although these variables are included into the state space. Entropy production as well as entropy-exchange are state functions. A classification of the different kinds of variables spanning the state space of a discrete system is achieved.