Field thermodynamic potentials and geometric thermodynamics with heat transfer and fluid flow

In order to treat the effects of local nonequilibrium in fluids the thermodynamic metric, previously used for measuring dissipation, is extended from a space of extensive state variables into a space of the field variables involving nonequilibrium quantities such as heat flux. The metric is investigated in the context of the field description of transport and flow phenomena off but close to equilibrium. Thermodynamic potentials and corresponding tensors are constructed on the basis of the extended Gibbs equation involving heat and macroscopic velocity terms. An extension of the theory is suggested to the problem of multicomponent heat and mass diffusion.