Dynamics on differential one-forms

Mathematical models of dynamics employing exterior calculus are shown to be mathematical representations of the same unifying principle; namely, the d escription of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exter ior calculus, to a set of characteristic differential equations and a chara cteristic tangent vector which define transformations of the system. This p rinciple, whose origin is Arnold's use of exterior calculus to describe Ham iltonian mechanics and geometric optics, is applied to irreversible thermod ynamics and the dynamics of black holes, electromagnetism and strings. It i s shown that "exterior calculus" models apply to systems for which the dire ction of change is given by a characteristic tangent vector and "convention al calculus" models apply to systems whose direction of change is arbitrary . The relationship between the two types of models is shown to imply a tech nical definition of equilibrium for a dynamic system.