Detailed Balance For Systems With Irreversible Reactions
Detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process and required reversibility of all elementary processes. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc.), detailed mechanisms include both reversible and irreversible reactions. If one represents irreversible reactions as limits of reversible steps, then it become obvious that not all reaction mechanisms with irreversible reactions can be obtained as limits of systems or reversible reactions with detailed balance. For example, the irreversible cycle cannot be obtained as such a limit but the reaction mechanism can.
A system of reactions with some irreversible reactions is a limit of systems with detailed balance when some constants tend to zero if and only if (i) the reversible part of this system satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reactions. Physically, the last condition means that the irreversible reactions cannot be included in oriented cyclic pathways.
Read more about this topic: Detailed Balance
Famous quotes containing the words detailed, balance, systems and/or reactions:
“... every event has had its cause, and nothing, not the least wind that blows, is accident or causeless. To understand what happens now one must find the cause, which may be very long ago in its beginning, but is surely there, and therefore a knowledge of history as detailed as possible is essential if we are to comprehend the past and be prepared for the future.”
—Pearl S. Buck (1892–1973)
““... To say of one mask it is like,
To say of another it is like,
To know that the balance does not quite rest,
That the mask is strange, however like.””
—Wallace Stevens (1879–1955)
“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)
“Prolonged, indiscriminate reviewing of books is a quite exceptionally thankless, irritating and exhausting job. It not only involves praising trash but constantly inventing reactions towards books about which one has no spontaneous feeling whatever.”
—George Orwell (1903–1950)