The paper contains an outline of a new approach to the thermodynamics of irreversible processes. This approach is based on a fundamental inequality which is derived from the Second Law of Thermodynamics under the assumption that the material is, in a well-defined sense, thermodynamically stable. If one confines one’s attention to situations in which the intensive parameters deviate only little from their original equilibrium values, one can invoke the well-developed mathematical theory of linear passive systems, and one arrives at very general statements on continuous materials. An important feature of this approach consists in the fact that the value of the entropy in non-equilibrium states does not appear in the equations. Therefore, there is no need to specify it by special and questionable assumptions. It is also possible to cast the equations governing the irreversible processes in a form which introduces appropriate internal variables. This leads to a thermodynamic formalism with a well-defined entropy even in nonequilibrium states. The latter is also a thermodynamic potential in the proper variables and leads to a nonnegative entropy-production term. This formalism satisfies the principle of local state or, equivalently, is deterministic in the sense that a complete knowledge of the state at time t1 and of the interaction of the system with the surroundings for t ≥ t1 permits us to predict the future development of the system without the need to endow the material with a memory.

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