ARTICLES 



EVOLUTION AND IRREVERSIBILITY 



By ALFRED J. LOTKA, M.A., D.Sc. 



The recent publication in Science Progress of Dr. Petro- 

 nievics's article, " Sur la loi de revolution irreversible," l 

 seems to furnish an opportune occasion for a discussion of the 

 relation between irreversibility as understood by the physicist, 

 and evolution as conceived more particularly by the biologist. 



Biology leaves us with a not very clearly defined idea of 

 progression as one of the fundamental characteristics of those 

 changes which are embraced by the term " evolution." Such 

 phrases as " the passage from lower to higher forms," which 

 are often employed to describe evolution, are vague, and 

 undoubtedly contain an anthropomorphic element. 2 The fact 

 seems to be that all we can predicate positively to-day is that 

 evolution is a " unidirectional " change in time. 



Now, the physicist is well acquainted with unidirectional 

 changes. They are precisely those changes which he terms 

 " irreversible." And, for certain cases at least, he is able 

 to define in precise terms the direction of evolution. For 

 example, in an isolated physical system evolution proceeds in 

 such direction that the entropy of the system increases. More 

 generally, if the state of a physical system is defined in terms 

 of certain variables X lt X 2 . . ' . X n and certain parameters 

 Pi, P 2 . . . P m , and if evolution is allowed to proceed (i.e., 

 if the X's are allowed to change by a spontaneous process) 

 while keeping the parameters P constant, then certain definite 

 and known functions of the variables X and of the parameters 



1 January 191 9, p. 406. 



1 " Evolution is thus almost synonymous with progress, though the latter term 

 is usually confined to processes of development in the moral as distinguished from 

 the physical world. Further, this idea, as Mr. Spencer remarks, has rather a 

 subjective than an objective source, since it points to an increased value in exist- 

 ence, as judged by our feelings" {Encyc. Brit., 9th edition, vol. viii, pp. 751-2). 



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