Irreversible Thermodynamics

There are alternative sets of postulates which yield entirely equivalent results for several important theories. In such cases the choice of a particular set of postulates may be based upon mathematical simplicity, close relationship to experiments or to the nature of the theory, or merely personal taste. While the postulate of conservation of energy is usually presented in similar form for thermodynamics or statistical mechanics, the form of the postulate comprising the second law is commonly very different. In thermodynamics the postulate may be in terms of the impossibility of an isothermal engine producing work at the expense of heat while in quantum statistical mechanics one postulates equal a priori probability for all individual quantum states. It is the purpose of the present paper to point out that there are such alternatives for the additional postulate necessary to derive the Onsager equations for the irreversible thermodynamics of processes in the linear rate law region near equilibrium. The heat engine, which was the primary subject of interest during the original development of classical thermodynamics, comprises both reversible and irreversible processes. In such machines the separation of the reversible changes of the working fluid from the frictional effects and the irreversible heat leaks is practically self-evident. Thus in his classic paper" On the dynamical theory of heat", Kelvin! assumes this separation of processes to be obvious in ordinary heat engines where he simply specifies " perfect engine", but he discusses the separation at length for thermoelectric phenomena as a separate postulate. The magnificient work of Gibbs, van't Hoff, and others, showing the applicability of thermodynamics to physicochemical equilibria distracted attention for a time from steady-state problems. But in 1926 Eastman" applied Kelvin's method to thermo-osmosis, the Soret effect, and the properties of thermocells. Wagner3 and Londonused similar methods soon thereafter. In these treatments it is assumed that the irreversible heat flow constitutes a process which is independent of the processes transferring the material components. Then the second law of thermodynamics requires the entropy to be a maximum with respect to any transfer ofmatter and thus determines the steady-state distribution. The new formulation of the near-equilibrium problems in 1931 by Onsager! in terms of linear rate laws and his derivation of the reciprocal relationships gave new impetus to theoretical work and de Groot", Prigoginc? and others soon applied this new formulation to a wide variety of phenomena. It was implied in some of these treatments that the new methods were more rigorous in spite of the fact that in so far as the problems had been treated previously by Kelvin's methods, the results were identical. However, the