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:
“Of course we will continue to work for cheaper electricity in the homes and on the farms of America; for better and cheaper transportation; for low interest rates; for sounder home financing; for better banking; for the regulation of security issues; for reciprocal trade among nations and for the wiping out of slums. And my friends, for all of these we have only begun to fight.”
—Franklin D. Roosevelt (1882–1945)
“The principle that human nature, in its psychological aspects, is nothing more than a product of history and given social relations removes all barriers to coercion and manipulation by the powerful.”
—Noam Chomsky (b. 1928)
“Modern tourist guides have helped raised tourist expectations. And they have provided the natives—from Kaiser Wilhelm down to the villagers of Chichacestenango—with a detailed and itemized list of what is expected of them and when. These are the up-to- date scripts for actors on the tourists’ stage.”
—Daniel J. Boorstin (b. 1914)
“They relieve and recommend each other, and the sanity of society is a balance of a thousand insanities. She punishes abstractionists, and will only forgive an induction which is rare and casual.”
—Ralph Waldo Emerson (1803–1882)