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The mesoscopic concept in continuum mechanics consists of extending the domain of the balance equations by the set of mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. The balance equations defined on this extended domain and an example concerning liquid crystals of biaxial molecules are discussed.

A comparison is made between two classical methods for the exploitation of the second law of thermodynamics: the Coleman-Noll and the Liu procedure. On the example of a rigid heat conductor with general entropy flux, it is shown that the two procedures are equivalent. This equivalence is demonstrated in the case of a state space including the wanted fields, only, as well as in the case of gradients being relevant for constitutive equations, too. Also, the possible importance of an internal variable or an internal degree of freedom is considered.

Governing equations of dissipative generalized solid mechanics are derived by thermodynamic methods in the Piola-Kirchhoff framework using the Liu procedure. The isotropic small strain case is investigated in more detail. The connection to the Ginzburg-Landau type evolution, dual internal variables, and a thermodynamic generalization of the standard linear solid model of rheology is demonstrated. Specific examples are chosen to emphasize experimental confirmations and predictions beyond less general approaches.

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