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:
“They had both noticed that a life of dissipation sometimes gave to a face the look of gaunt suffering spirituality that a life of asceticism was supposed to give and quite often did not.”
—Katherine Anne Porter (1890–1980)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)