On the thermodynamics of semi-systems with restrictions on the accessibility of states

A mathematical system is developed in which caloric functions of state such as entropy and free energy are presented in terms of two elements: topological space, Sigma, and a set of processes, Pi. State transformations are induced by the processes, and semi-systems including: elastic and viscous materials, materials with fading memory, perfectly plastic materials, and certain materials with internal state variables. These are described by a set of equations in terms of the two element system. Attention is given to the Clausius property, in which every state is a base state.