We deal with those thermodynamical transport processes in which the current densities are proportional to the gradient of the intensive quantities. We introduce a 'potential function' to the intensive quantities so that by its help a Lagrangian and a variational principle of classical type can be constructed. The analogon of the energy momentum tensor, i.e. the thermodynamical tensor, and the canonically conjugated quantities are derived.
We introduce an abstract scalar field and a covariant field equation, by which we make an attempt to connect the Fourier heat conduction and wave-like heat propagation. This field can be the generalization of the usual temperature from a dynamical point of view. It is shown that a kind of effective mass of this thermal process can be calculated. Finally, we express the unit of dissipative action with the help of universal constants.
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