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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.

In this paper, we present a method by which it is possible to describe a dissipative system (that is modeled by a linear differential equation) in Lagrangian formalism, without the trouble of finding the proper way to model the environment. The concept of the presented method is to create a function that generates the measurable physical quantity, similarly to electrodynamics, where the scalar potential and vector potential generate the electric and magnetic fields. The method is examined in the classical case; the question of quantization is unanswered.

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