5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 65 



For 7",,. we have similarly 



00 00 



-T| -T< 



00 "1 / " 



= d 



Since ^— = Z>,( 1 — 



dyi '\ \+yu 



we can write 



0',+ r,.)^^^_ = (^,.+ l)^+(r,.-l)- 



e,- '■ ^'^ Qi A,+k,Y, 

 in the original variables. Therefore we get the result 



bjki 



Q 



'i^^A-^] 



= d (32) 



These results are equipartition theorems, analogous to the equipartition 

 of kinetic energy among all degrees of freedom in physical systems. They show 

 us that the mean Tfor any variable in the epigenetic system is the same as for 

 any other. In other words, the total T of the system is in the mean equally 

 distributed among all variables. This is the mathematical side of the argument 

 presented at the beginning of this chapter, where it was indicated how the epi- 

 genetic components interact through common metabolic pools so that the 

 quantity G, talandic energy, is exchanged and distributed throughout the 

 whole system. 



What we see from the relations (31) and (32) is that the condition of zero 

 talandic temperature, ^ = 0, occurs when all the variables Xj, 7, are at their 

 steady state values and there are no oscillations. (Another set of values giving 

 6 = 0, is Xi = 0, y, = 0, the null solution, which is trivial since it means that 

 we have no system at all.) As d increases, the size of the oscillations increases, 

 so that talandic temperature is a measure of the degree of excitation of the 



