From experiment there are strong indications that the flux of particles \( j(x,t) \), viz., the number of particles passing \( x \) at a time \( t \) is proportional to the gradient of \( w(x,t) \). This proportionality is expressed mathematically through $$ \begin{equation*} j(x,t) = -D\frac{\partial w(x,t)}{\partial x}, \end{equation*} $$ where \( D \) is the so-called diffusion constant, with dimensionality length$^2$ per time.