n THEORGANISMASANOPENSYSTEM 1 53 



electrical currents, chemical reactions, etc. — called Jluxes — are assumed to be 

 caused by generalized forces such as temperature gradients, concentration gra- 

 dients, electrical potentials, chemical affinities, etc. Such irreversible process can, 

 as a rule, be expressed by proportionalities between the rate of flow and the corre- 

 sponding force. Examples are Fourier's law for heat flow and temperature gradient, 

 Pick's law for diffiision and the concentration gradient. Ohm's law for electrical 

 current and electromotoric force, etc. This can be written in a general form: 



J = LX (2.17) 



where J is the flux. A' the force, and L a scalar parameter such as heat or electrical 

 conductivity, diffiision coefficient, the chemical "drag" coefficient, etc. 



Considering two fluxes and two forces, we find so-called reciprocal phenomena 

 such as the Soret eflfect, i.e. the formation of a flow of matter due to a temperature 

 gradient (thermodiffusion) and the Dufour effect, i.e. a flow of heat due to a 

 concentration gradient (diffusion-thermo eflfect). Suppose there is a flow of 

 energy the rate of which is J\, and a flow of matter, with a rate Ji- If these 

 processes take place independently, they will follow the phenomenological 

 relations and can be considered as being due to the thermal force X\, and the 

 diffiision force X2, respectively, with the appropriate parameters L. If, however, 

 both processes take place simultaneously, it may be assumed that each flux 

 depends on both forces present. Retaining the assumption of linearity, we have : 



Ji = Ln A'l + LnXil ^^^^^^ 



Ji = L21 X\ + L22 X2 S 



J. Now we come to the third and decisive step, the Onsager reciprocal relations. 

 The coefficients Ln and L21 indicate the coupling or the interaction of both 

 processes. The Onsager relations state an equality of these coupling coefficients, 

 so that in the particular case mentioned : 



L12 = L21 (2.19) 



That is, there is a symmetry of the eflfect of the diffiision force on heat flow, and 

 the effect of the thermal force on diffiision. 



These formulations can easily be generalized from the consideration of two to 

 any number of interacting forces and fluxes. 



The reciprocal relations apply provided that the thermodynamic forces are 

 suitably chosen. This, according to Onsager, means that the forces are chosen 

 in such way that if any flux J is multiplied by the corresponding force X, the 

 sum of the products is equal to entropy production multiplied by absolute 

 temperature : 



Ta = JiX, + J2X2 + . . . = SJ,Z, (2.20) 



/ 



For example, in a chemical reaction entropy production per unit volume and unit 

 time is defined by: 



Ta = ILAfli (2.21) 



i 



Lilerature p. 253 



