146 Information Storage and Neural Control 



dS = k (J3d <e> + aa d <Ha> + "& d <nb> + . . . 



If two systems with different values of /3, «„, a^, . . . , and witli 

 total energy and matter constant between them, are allowed to 

 interact irreversibly, then the energy gain of one must be equiva- 

 lent to the loss of the other, and the gain in n,j, n,^^ . . . by one 

 corresponds to that lost by the other. In the language of game 

 theory (23) such a relationship is zero-sum. \idXi = dX-i = . . . =0, 

 then the connected system's entropy change is, from [17], 



[18] dS - k [(j3 - 13') d <€> + {aa - aa) d <Ha> 



+ (ab — ab') d <nb> + . . .] 



Hence, it is possible for one of the systems (call it community) 

 to decrease its entropy at the expense of the other (environment) 

 since the only requirenient is that dS > overall. 



Details of energy-matter exchange between such systems are 

 very complex because the parameters 3, aa, at, ■ . . may become 

 reciprocally coupled within a system 



d<e> _ _ a"Qo 



[19] ) {a,b,c, . . .) 



d<na> _ 



6/3 ~ ' daa dl3l 

 SO that 



[20] d<e> = -^ dl3 - -^ daa (a,b,C, ...) 



and 



d^- " dl3 daa 



d''QiO ,,, 3"Qo 



[21] d<na> = - T ~dl3 - ~r—;daa {a,h,c, . . .). 



daa dp daa" 



The important point to distinguish for our present purpose is that 

 for one system to diminish its entropy with respect to another 

 with which it is coupled in communication, it must establish and 

 maintain physical barriers to the free exchange of energy and 

 matter. In short, it must proliferate structural heterogeneity by 

 maximizing the inequality of the /^,'s in [10]. 



At the community level, such heterogeneities are maintained 

 by a graded series of discrete, functional barriers ranging from, at 



