Transformation of forces and flows

The phenomenological coefficients are not a function of the thermodynamic forces and flows on the other hand, they can be functions of the parameters of the local state as well as the nature of a substance. The values of Lik must satisfy the conditions 

The matrix of phenomenological coefficients Lkl and Kki are related by K = L 1 where L 1 is the inverse of the matrix L. In a general matrix form in terms of the conductance Ltj and resistance Ktj coefficients, Eq. (3.178) becomes 

This relation suggests that the local rate of entropy production is a quadratic form in all forces and in all flows if the cross coefficients differ from zero. 

Consider a system in which the thermodynamic forces are independent, while the flows are linearly related 

If the constants are nonvanishing, yk / 0, then we have the flow for component n 

---

The form of the expressions for the rate of entropy production does not uniquely determine the thermodynamic forces or generalized flows. For an open system, for example, we may define the energy flow in various ways. We may also define the diffusion in several alternative ways depending on the choice of reference average velocity. Thus, we may describe the flows and the forces in various ways. If such forces and flows, which are related by the phenomenological coefficients obeying the Onsager relations, are subjected to a linear transformation, then the dissipation function is not affected by that transformation. 

Example 3.11 Transformation of phenomenological equations dependent flows Transform the thermodynamic forces and flows when the forces are independent, while the flows are linearly dependent in a two-flow system 0 y./t +J2. 

Example 3.13 Transformation of phenomenological equations dependent flows and forces Transform the... 

---