Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.