Classical axiomatics with extension to nonequilibrium thermodynamics

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An attempt is made to reorganize the axiomatics of classical thermodynamics as written by Caratheodory in 1909 and to extend it to nonequilibrium systems. The three thermodynamic laws are derived from axioms and the entropy appears as the constant of integration of the Pfaffian equation with a suitably chosen integrating factor. Transition to nonequilibrium systems is shown to require an extension of the phase space to include the gradients of temperature and velocity as additional coordinates. Accessible states then have to comply with a system of momentum equations and any departure from these restrictions leads to inaccessible states.