In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954) and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013) we consider the entropy production and other thermodynamical quantities, such as the e...