5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 71 



We now obtain the "talandic free energy", i/r, which is defined by 



-jS0 = logZ (38) 



= S (logZ^,. + logZ,,) 

 1=1 



+\^b^-i^bi+i)iog^b,+\ogri^bi+i, 



Hence 



[iS^- 



^M,^ 

 e, y 



1=1 



j(2log|+log£r/c|-.,^^2 



>/c[-p,y( 



^<^.1 



+ 



^^iog^^.-^.-Jiogr(^^.+ i, ^-^j 



(39) 



- S {'A^.+'AJ 



/=i 



The "internal energy" function is defined as the mean value of G, hence 

 aiogZ 



G = 



d^ 



g-^ciprl2 



+ 



[-i-^.iog/S6,+ ^iogr(^^.+ i, ^^'■'^' 



a/s 



Qi 



+ 



i+^.iog^z.,-^iogr(i5^.+ i, ^-^'^ 



(40) 



/=1 



