152 GROWTH — - PRINCIPLES AND THEORY 2 



death when all energy is dissipated into uniformly distributed heat of low tempera- 

 ture, and the world process comes to a stop. In contrast, living nature shows a 

 ' transition toward higher order, heterogeneity, and organization. This is obvious 

 in embryonic development, when the ovum, a nearly homogeneous droplet of 

 protoplasm, eventually yields an organism of enormous complexity. It is equally 

 true of evolution which proceeds, in geological periods, from simple creatures to 

 ever higher forms of organization. 



In order to evaluate this problem, the limitations of conventional or "classical" 

 thermodynamics have to be contemplated. It almost exclusively deals with states 

 of equilibrium, processes in isolated systems, and transitions from one equilibrium 

 state to another. According to definition, the first and second principle of thermo- 

 dynamics apply to closed systems, stating that energy is constant and entropy 

 increases in such systems. They tell nothing about systems which are open, that is, 

 where there are processes of flow across the boundaries of the system. Classical 

 thermodynamics, therefore, should more adequately be denominated as thermo- 

 statics. It is inadequate where states of non-equilibrium, processes of material flow, 

 and irreversible processes are concerned. 



This situation has led to a modern development and generalization known as 

 Irreversible Thermodynamics (monographs: Prigogine, 1947; De Groot, 1951; 

 Denbigh, 1951; Haase, 1951-53, 1952)- 



[h) Principles of irreversible thermodynamics 



While a detailed presentation of this field is beyond the scope of the present 

 study, the basic concepts of irreversible thermodynamics will be briefly outlined 

 in view of the crucial problem of organic development indicated above. 



1. The first basic concept of irreversible thermodynamics is the introduction 

 of generalized thermodynamic functions which are not restricted to closed systems, 

 but take account of the energy transport in open systems. In every closed system 

 where irreversible processes take place, entropy must increase according to the 

 function : 



d^^o (2.15) 



In an open system, entropy can change for two reasons : by transfer of entropy 

 from outside into the system, and by production of entropy within the system. 

 This is expressed in the generalized entropy function of Prigogine: 



dS = d,^ + d,.S' (2.16) 



dgS is the change of entropy by transfer, d,.S' the production of entropy due to 

 irreversible processes in the system, such as chemical reactions, diffusion, heat 

 conduction, etc. Entropy production, djS, is always positive according to the 

 second principle. Entropy transfer, d^^*, however, may be positive, zero, or 

 negative. It is negative when, e.g., materials rich in free energy are introduced 

 into the system. Consequently, change of total entropy, dS, in an open system 

 can — depending on the sign and quantity of d^^* — be negative as well as positive. 



2. A second basis of irreversible thermodynamics is the supposition of the 

 so-called pheno?7ienological laws. Irreversible processes such as heat flow, diffusion, 



