Complex balance (source code)

= Complex balance
{title2=$\sum_{y'\to y}k_{y'\to y}c^{y'}=\sum_{y\to y'}k_{y\to y'}c^y$}

At a positive concentration vector $c$, the total incoming deterministic reaction flux equals the total outgoing flux at every <reaction complex>. Here $c^y=\prod_i c_i^{y_i}$ is the <law of mass action> monomial. This is stronger than balancing net production of each <chemical species>, but does not require pairwise <detailed balance> between reverse <chemical reactions>. A directed cycle can have nonzero circulation while satisfying complex balance.