7. STATISTICAL PROPERTIES OF THE EPIGENETIC SYSTEM 1 15 



Therefore the most probable value of .Vi is a quantity greater than/jj, and the 

 larger 6 the larger this most probable value. 



On the other hand, the most probable value o(yi is defined by the maximum 

 of 



which is readily observed to be yi = 0. Similarly, the most probable ^2 is 0, 

 so that 



[yi] = gi, [Y2] = g2 



The theorem on the equipartition of talandic energy among all degrees of 

 freedom is readily established for the strongly coupled system. We have in 

 this case 



00 00 00 00 



-Pl -pi —pi — P2 



00 



= -^ J^JlCvi+z^O^-^^-^O-^. 



-Pi 

 00 



- j e-^^'^^^dxAj e-^^^^^^dxidx2 



-Pl J -pi -p.. 



CO 00 



G \ \ e'^^^^^^dx^dx2 



— Pl — Pa __ a 



00 00 



f J e'^^^^'-dxidxz 



—pi -pi 

 Similarly we get 



These relations hold at equilibrium in the epigenetic system, when the oscil- 

 latory motion or more correctly the talandic energy is equally distributed 

 among all components. In terms of the original variables the equalities are 



d = Xi[hni^i-Pi) + hi2{^2-P2)] = X2[hu(^i-Pi) + h22iX2-P2)] 



Ai+kn Yi + ki2 Y2 

 = "^ f\\\^''J'^ [^2i( Y, -q,) + k22i Y2-q2)] (64) 



^2 + «21 Yi + k22 Y2 



