Dissipation in Systems With Semi-detailed Balance
Let us represent the generalized mass action law in the equivalent form: the rate of the elementary process
is
where is the chemical potential and is the Helmholtz free energy. The exponential term is called the Boltzmann factor and the multiplier is the kinetic factor. Let us count the direct and reverse reaction in the kinetic equation separately:
An auxiliary function of one variable is convenient for the representation of dissipation for the mass action law
This function may be considered as the sum of the reaction rates for deformed input stoichiometric coefficients . For it is just the sum of the reaction rates. The function is convex because .
Direct calculation gives that according to the kinetic equations
This is the general dissipation formula for the generalized mass action law.
Convexity of gives the sufficient and necessary conditions for the proper dissipation inequality:
The semi-detailed balance condition can be transformed into identity . Therefore, for the systems with semi-detailed balance .
Read more about this topic: Detailed Balance
Famous quotes containing the words dissipation, systems and/or balance:
“But there are other things than dissipation that thicken the features. Tears, for example.”
—Rebecca West (1892–1983)
“What is most original in a man’s nature is often that which is most desperate. Thus new systems are forced on the world by men who simply cannot bear the pain of living with what is. Creators care nothing for their systems except that they be unique. If Hitler had been born in Nazi Germany he wouldn’t have been content to enjoy the atmosphere.”
—Leonard Cohen (b. 1934)
“As the House is designed to provide a reflection of the mood of the moment, the Senate is meant to reflect the continuity of the past—to preserve the delicate balance of justice between the majority’s whims and the minority’s rights.”
—Lyndon Baines Johnson (1908–1973)