200 Herman Branson 



If the concentration within is stabihzed in such a manner that for a sUght 

 change the system returns to the resting value following the equation 



(1/Q) dCJdt = -a (8) 



where a is analogous to the rate constant appearing in equation (2), equation (7) 



may be written 



dN 

 i^ = A: — in Co/C, + kN^- (9) 



Equations (8) and (9) seem harmonious with equation (2) interpreted as being 

 applicable to the resting case when there is no net transport or to actual trans- 

 port with the condition that Cq — Q. 



The application of equation (9) to a fluctuation should follow this sequence. 

 Initially Cq = Q, and AA'^ particles jump from one solution to the other. 

 The rate of negentropy production or the rate of production of information 

 is /^ = A///A? = k^Noi. At the end of this fluctuation equation (9) becomes 

 for the next fluctuation kANcc 



IC -1- AC\ 

 n = A:(AA^/A/) In L I ^ J + k^N^. (10) 



Suppose that the next fluctuation is the movement of A A'' particles in the direction 



opposite to the first fluctuation in the same interval of time, A?. We should 



expect fi to be the negative of its original value. Expressing the logarithm 



1 + AC/C 

 in equation (10) as In -j . , and making use of the relation 



In 1^ = 2(A' + A-^/S + • • •), for X'' <\, 



the equation becomes 



ii^lk AMI At AC/C + kAN(x 

 but 



AN I At AC/C = ANIC AC/ A/ = -AA^a 



from equation (8), and since AC is negative in the second fluctuation. 



Finally: AH = —kANoL At. 



Thus the system returns to the equilibrium position on the entropy surface 

 with an increase in entropy exactly equal to the decrease of entropy experienced 

 in the first fluctuation. 



Analysis for Charged Particles 



In the derivation of the basic equations (6) and (7), the chemical potential 

 was employed, which limits the applicability of the analysis to uncharged 

 particles. To derive the corresponding equations for an ion, the electrochemical 

 potential /li' replaces ju, 



fx' = juq' + RT\na-^ZF(i> 



where Z is the valence, F is the Faraday, and is the potential. Substituting 



