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)
“Major [William] McKinley visited me. He is on a stumping tour.... I criticized the bloody-shirt course of the canvass. It seems to me to be bad “politics,” and of no use.... It is a stale issue. An increasing number of people are interested in good relations with the South.... Two ways are open to succeed in the South: 1. A division of the white voters. 2. Education of the ignorant. Bloody-shirt utterances prevent division.”
—Rutherford Birchard Hayes (1822–1893)
“[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)
“Success goes thus invariably with a certain plus or positive power: an ounce of power must balance an ounce of weight.”
—Ralph Waldo Emerson (1803–1882)