page_title: Tonti diagram
section_title: The birth of the classification diagram
hierarchical_section_title: Tonti diagram / The birth of the classification diagram
caption_attribution_description: English: Tonti diagram for electrostatics
context_page_description: The Tonti diagram, created by the Italian physicist and mathematician Enzo Tonti, is a diagram that classifies variables and equations of physical theories of classical and relativistic physics. The theories involved are in its construction are particle dynamics, analytical mechanics, mechanics of deformable solids, fluid mechanics, electromagnetism, gravitation, heat conduction, and irreversible thermodynamics. The classification stems from the observation that each physical variable has a well-defined association with a space and a time element, which can be grasped from the corresponding global variable and from its measuring process.
context_section_description: The fact that physical variables are associated with space and time elements endowed with inner or outer orientation and that space and time elements of a primal and a dual cell complex can be classified as shown on the right-hand side of Figs. 3 and 4, suggests a corresponding classification of physical variables. 
  Consider, as an example, the classification diagram of electrostatics, shown in Fig. 6. The left column includes those physical variables associated with the primal cell complex, whose elements are endowed with inner orientation: these are the configuration variables. The right column includes those physical variables associated with the dual cell complex, whose elements are endowed with outer orientation: these are the source variables.
  The equations linking the variables are contained in the rectangular boxes. The equations in each vertical column are balance equations, circuital equations and gradient-forming equations. They have a topological structure and are called topological equations. Those that link configuration variables to source variables—contained in the horizontal links—are material or constitutive equations, and belong to the category of phenomenological equations.
caption: Figure 6. Classification diagram for electrostatics.
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