486 SESSION V. DISCUSSION 



Thermodynamics has, however, a greater general applicability than kinetics, in that it 

 does not make use of a hypothetical model of the process. On the other hand, a linear 

 approximation is, undoubtedly, useful even for an understanding of non-linear processes. 

 Physics shows a number of examples of situations of this sort — for example, in the theory 

 of the perturbations of anharmonically related systems. Finally, irreversible biochemical 

 processes take place by stages, and for each stage the deviations of energy from equili- 

 brium may not be large, although the process as a whole may be very far from being in 

 equilibrium. I do not, therefore, feel that the criticism contained in Eyring's work really 

 precludes the application of irreversible thermodynamics to biology. Naturally, if we 

 follow this course, we must observe caution. 



At the same time, there are great possibilities for the development of non-linear thermo- 

 dynamics of irreversible processes. Prof. Prigogine's paper contains valuable new ideas 

 in this field. 



Recently it has been emphasized in the literature (in particular in the works of Prof. 

 Prigogine) that an organism growing under normal conditions is in a stationary (though, 

 naturally, not in a static) thermodynamic state. In the light of the new ideas put forward 

 by Prof. Prigogine it is becoming obvious that this is only a rough approximation. Of 

 course, in real biological processes both cycles and spiral approximations to and deviations 

 from the stationary state are to be found. There is, for example, the cycle of sleeping and 

 waking, or the cyclic changes in the numbers of populations of plants and animals caused 

 by interspecies or, mainly, by intraspecies competition. 



I should like to point out one interesting possibility of development of the theory. 

 That outstanding Soviet physicist, the late Academician Mandel'shtam, developed a 

 general theory of non-linear perturbations, the theory of the stability of perturbations. 

 I think that the further development of the ideas put forward by Prof. Prigogine can be 

 carried out along the lines of Mandel'shtam's theory on the basis of a mathematical 

 analogy between the equations of non-linear irreversible thermodynamics and the theory 

 of non-linear perturbations. This is a real physical problem which we hope to take up. 



I have already spoken here about the possibility of a detailed determination of the 

 specific peculiarities of macromolecules, as distinct from small molecules, which deter- 

 mine their biological roles. From the thermodynamic aspect too, there are corresponding 

 pecuharities. Polymeric chains have an enormous number of mechanical degrees of 

 freedom as well as chemical ones. Chemical reactions of macromolecules can be accom- 

 panied by mechanical processes of twisting or untwisting of the chain. Tliis gives a serious 

 possibility of concealing a deficit in free energy in biochemical processes. Finally, even 

 processes which take place at a supramolecular level must be accompanied by chemical 

 processes. Aggregation of macromolecules into bundles, their crystallization and mutual 

 orientation as well as the opposite processes, must play a part, along with chemical reac- 

 tions, in the cell. In this respect the cycle of spiralization of the chromosomes is a com- 

 ponent part of the chemico-biological cycle. 



In conclusion, I should Uke to affirm my conviction that 'irreversible thermodynamics' 

 can be applied with advantage, not only to the life of the individual organism, but also 

 to the process of evolution as a whole. From a mathematical point of view this process is 

 a network of the probability chains of Markov. From the point of view of thermodynamics 

 both the biosphere as a whole and its individual parts are open systems the development 

 of which can be characterized by the rate of change of entropy. 



Of course, 'irreversible' thermodynamics cannot explain the origin of life. Thermo- 

 dynamic analysis is, however, absolutely necessary for the solution of this problem. 



A. G. Pasynskiï (U.S.S.R.): 



The Application of Thermodynamics to Biology 



{with reference to Prof. Prigogijie's paper) 



Studies of the theory of irreversible chemical processes are of great importance for 

 biochemistry and, in this respect, the thermodynamic studies of Prof. Prigogine are of 

 fundamental interest, especially his principle of the minimal rate of production of entropy 



