Onsager Reciprocal Relations and Detailed Balance
Let the principle of detailed balance be valid. Then, in the linear approximation near equilibrium the reaction rates for the generalized mass action law are
Therefore, in the linear approximation near equilibrium, the kinetic equations are :
This is exactly the Onsager form: following the original work of Onsager, we should introduce the thermodynamic forces and the matrix of coefficients in the form
The coefficient matrix is symmetric:
These symmetry relations, are exactly the Onsager reciprocal relations. The coefficient matrix is non-positive. It is negative on the linear span of the stoichiometric vectors .
So, the Onsager relations follow from the principle of detailed balance in the linear approximation near equilibrium.
Read more about this topic: Detailed Balance
Famous quotes containing the words reciprocal, relations, detailed and/or balance:
“I had no place in any coterie, or in any reciprocal self-advertising. I stood alone. I stood outside. I wanted only to learn. I wanted only to write better.”
—Ellen Glasgow (1873–1945)
“Happy will that house be in which the relations are formed from character; after the highest, and not after the lowest order; the house in which character marries, and not confusion and a miscellany of unavowable motives.”
—Ralph Waldo Emerson (1803–1882)
“[The Republicans] offer ... a detailed agenda for national renewal.... [On] reducing illegitimacy ... the state will use ... funds for programs to reduce out-of-wedlock pregnancies, to promote adoption, to establish and operate children’s group homes, to establish and operate residential group homes for unwed mothers, or for any purpose the state deems appropriate. None of the taxpayer funds may be used for abortion services or abortion counseling.”
—Newt Gingrich (b. 1943)
“Any balance we achieve between adult and parental identities, between children’s and our own needs, works only for a time—because, as one father says, “It’s a new ball game just about every week.” So we are always in the process of learning to be parents.”
—Joan Sheingold Ditzion, Dennie, and Palmer Wolf. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 2 (1978)