On the general structure of mathematical models for physical systems

Abstract: It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical states, a constitutive law that associates dynamical states with kinematical states, as well as a duality principle. The equations of motion or statics then come about from, on the one hand, specifying the integrability of the kinematical state, and on the other hand, specifying a statement that is dual to it for the dynamical states. Examples are given from various fundamental physical systems.