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:
“The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.”
—Herbert Spencer (1820–1903)
“The only people who treasure systems are those whom the whole truth evades, who want to catch it by the tail. A system is just like truth’s tail, but the truth is like a lizard. It will leave the tail in your hand and escape; it knows that it will soon grow another tail.”
—Ivan Sergeevich Turgenev (1818–1883)
“Bourgeois society is infected by monomania: the monomania of accounting. For it, the only thing that has value is what can be counted in francs and centimes. It never hesitates to sacrifice human life to figures which look well on paper, such as national budgets or industrial balance sheets.”
—Simone Weil (1909–1943)