Abstract
Let us remind ourselves of the aim of the ordinary thermodynamics of thermomechanical processes. The fields which are usually sought within such a description are either the map f describing the motion relative to a chosen reference configuration and the temperature T (Lagrangian description) or the mass density ρ, the velocity field v, and again the temperature T (Eulerian description). As we mentioned already, the Lagrangian description can be formulated equivalently for the deformation gradient F and the velocity field v instead of the map f. We show the list of those fields and the corresponding conservation laws in the juxtaposition in the table below.
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