Using the category theory approach, we start defining a class of objects that is the class of bodies in a state of equilibrium. Interaction is the set of morphisms between objects in the category. The action $I_{01}$ (a morphism) of an external body $\varPhi_1$ on the body $\varPhi_0$ generate internal process $I_{0}$ (an automorphism). A set of automorphisms are related with the ``natural'' tendency of the body to evolve to a new equilibrium state that came's the measure of some property in $\varPhi_1$.  The notion of equilibrium is central and based on a dual relationship between two opposite categories. An equilibrium state is described by a set of scalar fields related with the observation process or during a modelling process. Then the system is described by an algebra over a field $\F$, an $\F-albebra$. Intensive and extensive physical properties and observer algebras are studied and some applications of the theory are discussed.