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∫

_{∂V}

**J⋅dS**=-d/dt∫

_{V}p(

**r**,t)dV

The flux can be written as a sum of convective and diffusive terms

**J**=p(

**r**,t)v(

**r**,t)-D(

**r**,t)

**∇**p(

**r**,t)

and substitution of this with use of the divergence theorem yields

∂

_{t}p(x,t)=-∂

_{x}[p(x,t)v(x,t)]+∂

_{x}[D(x,t)∂

_{x}p(x,t)]

where I have moved to one dimension for simplicity.

However the form found here

https://en.wikipedia.org/wiki/Fokker–Planck_equation

is given as

∂

_{t}p(x,t)=-∂

_{x}[p(x,t)v(x,t)]+∂

_{x}

^{2}[D(x,t)p(x,t)]

I was wondering if anybody would be able to help me account for this difference. Thanks!