Particle current ($J_N=-d{N}_L/dt$)

The rate at which particles cross an oriented surface, measured as particle count per unit time. If a local continuity equation has number density $n$ and current density ${\mathbf{j}}_N$, then ${\partial }_{t}n+\nabla \cdot {\mathbf{j}}_N=0$ and $J_N={\int }_S{\mathbf{j}}_N\cdot d\mathbf{S}$. In a closed two-reservoir system, a left-to-right particle current is $-d{N}_L/dt=d{N}_R/dt$. Neutral particles carry this current without an associated electric current.