Geometrical Thermodynamic Field Theory

A manifestly covariant, coordinate independent reformulation of the Thermodynamic Field Theory (TFT) is presented. The TFT is a covariant field theory that describes the evolution of a thermodynamic system, extending the near-equilibrium theory established by Prigogine in 1954. We introduce the {\it Minimum Dissipation Principle}, which is conjectured to apply to any system relaxing towards a steady-state. We also derive the thermodynamic field equations, which in the case of alpha-alpha and beta-beta processes have already appeared in the literature. In more general cases the equations are notably simpler than those previously encountered and they are conjectured to hold beyond the weak-field regime. Finally we derive the equations that determine the steady-states as well as the critical values of the control parameters beyond which a steady-state becomes unstable.