Abstract
Meixner’s historical remark in 1969 “... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined....” is investigated from today’s insight. Several statements—such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness—are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.
Highlights
The Second Law (SL) has many faces: there are different formulations in phenomenological thermodynamics, statistics, kinetics and quantum theory
The variables of the equilibrium subspace are determined by the Zeroth Law: The state space of a thermally homogeneous Schottky system in equiIibrium is spanned by the work variables, the mole numbers and the internal energy zeq = ( a, n, U )
With the aid of thermodynamic systems of the simplest kind, namely electrical networks, it can be shown that the concept of entropy in the absence of equilibrium is questionable but that it cannot even be defined
Summary
The Second Law (SL) has many faces: there are different formulations in phenomenological thermodynamics, statistics, kinetics and quantum theory. Carnot [5]: Reversible Carnot processes exist (not really, but as a mathematical closure of irreversible processes), and starting with these verbal statements of Kelvin, Clausius and Carnot, the following Clausius inequality valid for cyclic processes in closed systems can be derived [6] in an up-to-date formulation. T 2 is the thermostatic (equilibrium) temperature of the heat reservoir which controls the cyclic process. Beyond these questions, a shortcoming of the derivation of Clausius inequality (1) has to be taken into consideration: the statement of Carnot claims the existence of reversible processes, a presupposition which should not be used here, because the physical meaning of reversible processes is not evident and has to be defined properly in the course of this paper. Some of these formulations can be found in [8,9,10,11,12,13,14]
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