= Chemical diffusion matrix
{title2=$B=\sum_ra_r\nu_r\nu_r^{\mathsf T},\quad D_{ij}=B_{ij}/(\mu_i\mu_j)$}
A reaction's <stoichiometric vector> outer product multiplied by its <reaction propensity function> is its contribution to the infinitesimal state-increment covariance. Summing over channels gives $B$. Its normalized form $D$ divides by the two mean copy numbers. The <Fokker-Planck equation> writes the associated second-derivative term with $B/2$; the covariance evolution and normalized stationary Lyapunov equation instead use $B$ and $D$ themselves. A simultaneous unit loss of two species contributes positive cross noise even when their long-time stationary covariance is negative.
Back to article page