72 TEMPORAL ORGANIZATION IN CELLS 



The "talandic entropy" is 



S = -^-^ = logZ-^^^logZ = i {5,, + 5'^J 



Therefore 



= -^log?|-'+log£//c 



[-'^vmi 



(^')''/^,-e-^^'"''' 



2(l-log^2') + log£//c 



5^^ = logZ,^-^^logZ,^ 



(41) 



d^ 



= i3Z),-(i36,+ l)log^^ + logrhS^.+ l, 



/3Z>,^, 



+\i+^b^og^b^-^.Aogr^b^+\, 



= (i8^.+ i)-iogj8^+iogr(^^.+ i, ^'j-^^^iogr^^^.+ r 



(42) 



The entropy function has the important property that it measures larger 

 for systems in equilibrium, represented by the canonical ensemble, than the 

 corresponding quantity (-logp) for other states of the system given that the 

 mean value of G is fixed. This is interpreted to mean that non-equilibrium 

 states tend to decline into equilibrium ones of maximal entropy. In an epi- 

 genetic context fixed G means, roughly speaking, that there is a certain amount 

 of oscillatory activity throughout the whole system which is held constant. The 

 entropy theorem then tells us that there will be a "flow" or exchange of this 

 activity between different parts of the system until the condition of maximum S 

 is reached, at which point the system is at equilibrium and no further net flow 

 occurs between parts. There will of course still be fluctuations of G in parts of 

 the system ; and it should be emphasized again that for biological systems of the 

 type we are considering, where the number of degrees of freedom is in the 

 hundreds at best, and certainly not in the millions, fluctuations may be quite 

 considerable. There is also the more serious possibility that the heterogeneity 



