A simple example for comparing GENERIC with rational non-equilibrium thermodynamics

During the last 15 years a bracket formalism of dissipative continuum physics has been developed which resulted in a formulation which is shortly denoted as GENERIC. GENERIC has been applied to different problems of continuum thermodynamics, often in this way, that a well-known problem was reformulated in GENERIC formalism. To learn some more about the GENERIC procedure we consider a gas which is contained in a cylinder closed by a piston moving with friction. We treat this simple discrete system with rational non-equilibrium thermodynamics by using Liuʹs procedure and, for comparison, also with the GENERIC formalism. Both different procedures yield in the same results, especially in the same entropy production. Differences, similarities and fundamental presuppositions of both formalisms are discussed and compared.