FUNDAMENTALS OF DISSIPATION INEQUALITIES .1. DISCRETE-SYSTEMS

In order to develop phenomenological non-equilibrium thermodynamics the minimal state space in which non-equilibrium processes are describable is introduced. This is done by using the contact temperature, a non-equilibrium analogue of the thermostatic temperature. Because the equilibrium subspace is embedded in the minimal state space, non-equilibrium quantities which are state functions in equilibrium must satisfy an embedding axiom. Each non-equilibrium process in the minimal state space is accompanied by projections which are quasi-processes in the equilibrium subspace. Two of these projections are of special interest because together with a suitably defined non-equilibrium entropy and with Clausius’ inequality or its intensified formulation, the difference between them yields a dissipation inequality for discrete open systems. The relationship between this dissipation inequality and Meixner's is achieved by translation into field formulation. The result is that the physically undefined temperature of so-called rational thermodynamics can be replaced by the well defined contact temperature. The existence of an entropy production which is non-negative and locally in time is discussed. © Copyright by Walter de Gruyter & Co.