5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 77 



and that r, always enters the function Z,,. in the form/3f„ it is readily established 



that 



dt/f^. ^ \d\ogZp. ^l^ 



Similarly 9^. = ^"a/^r ' ^^''- 



Therefore we have 



and /',,.= -^.v.^.a7^= -^^'^^dir 



whence finally 



We see that the external parameters affect the system through the quantities 

 Ci and bi, causing changes in the steady state values of the variables and also 

 changes in the talandic functions 6, G, S, andifj. The talandic work done when 

 an external parameter s^ changes by an amount Ss^ is defined as 



Usr is a stimulus which acts for a period of time from /q to /i then the amount 

 of work done in connection with this stimulus is given by 



ti 







If 6 is held constant and the process is a reversible one we can write 



Ci(ti) CiUi) 



1=1 ^i..\ h.i,.\ 



CiUo) bi(lo) 



\i= 1 '=1 J 



= "Ao-'/'i 



