Abstract
There are several approaches to the theory of continuous materials in non-equilibrium. They are the classical thermodynamics of irreversible processes, the so-called general non-linear continuum theory based on the Clausius-Duhem inequality and a recent approach which uses instead a fundamental inequality which follows from a thrifty application of the Second Law. Merits and shortcomings of these theories are discussed. It is also explained that the concept of entropy in non-equilibrium has no foundation in a consequent continuum theory; no unique entropy can be defined nor evaluated from measured dynamic and thermodynamic data. Only if other information on the atomistic structure and on the molecular mechanisms is available, may the entropy be given a meaning outside equilibrium. We would therefore assert that the concept of entropy in non-equilibrium should be completely discarded when building up a general continuum theory. Only the third of the approaches mentioned above meets this requirement.
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