II THEORGANISMASANOPENSYSTEM 1 55 



This, however, is in no way generally the case. In particular, it does not hold for 

 the important case of open chemical reaction systems. The assumption that 

 reaction rate is a linear function of the thermodynamic force (difference of the 

 chemical potentials of reactants and end products of the reaction) is approximately 

 true only if the system is close to chemical equilibrium. In general, however, 

 reaction rate depends on concentrations rather than chemical potentials. It has 

 been shown by Denbigh (1952) that the discrepancy between concentrations 

 giving minimum entropy production and those of the steady state is considerable. 

 Hence, minimum entropy production does not define the steady state of an open 

 reaction system, and at present no simple thermodynamic definition of the latter 

 is available. The approach of an open chemical system toward a steady state is 

 determined rather by kinetic factors, namely, concentrations, than by thermo- 

 dynamic forces. 



Therefore, similarly as thermostatics has been generalized in (now conventional) 

 irreversible thermodynamics on the basis of the above-enumerated principles 

 further generalizations appear to be necessary. This applies i. to elimination of 

 the above-mentioned restrictions hitherto assumed in irreversible thermo- 

 dynamics, but also 2. to a deep-reaching paradox inherent in thermodynamic 

 theory. Entropy is, in Eddington's expression, the "Arrow of Time", the basic 

 function indicating the unidirectional flow of physical events. However, time does 

 not appear explicitly in the equations of thermodynamics, classical or irreversible. 



An interesting attempt toward such generalization was made by Reik (1953)- 

 Reik introduces a "time axiom" which appears to be the most general expression 

 the second principle has found hitherto. Reik's time axiom i. gives the classical 

 laws for thermodynamic equilibrium if time approaches infinity; 2. If the equations 

 of the time axiom are developed into series for the Onsager forces and the equilib- 

 rium state and only the linear terms are retained, the phenomenological laws 

 and reciprocal relations follow as a first approximation; j. The time axiom is, 

 however, more general because it is not restricted to near-equilibrium states, but 

 also is applicable to states of non-equilibrium, and indicates the time-laws for 

 irreversible processes. 



(?) Entropy and the living world 



Irrespective of these problems, it can be stated that, as previously mentioned, 

 irreversible thermodynamics has been elaborated for numerous problems in 

 physics. In the more difiicult and fascinating problems of biophysics, several 

 attempts to apply thermodynamic considerations to open systems have been 

 made, such as in the energetics of metabolizing systems (p. i49ff.); the active 

 transport by the living cell in contrast to passive penetration based upon diffusion, 

 distribution, or osmotic equilibria; bioelectric potentials, etc. 



Bypassing such special problems, the apparent contradiction to physical law 

 in the living world can be given a precise answer {cf. Bertalanffy, 1951a, 1953; 

 Haase, 1951, 1957; Jung, 1956). The alleged contradiction between entropy and 

 evolution and the seeming violation of the second principle in the living world 

 does, in fact, not exist or rather, it disappears with the generalization of physical 

 theory. Entropy must increase in all irreversible processes. Therefore, the change 



Literature p. 253 



