Entropy of Diffusion: Delta Initial Condition

[simoncks]

Homework Statement

The problem requires me to find the entropy of a diffusion constant as a function of time (I guess in terms of diffusion coefficient)

Homework Equations

Perhaps Heat / Diffusion kernel
S = k p lnp

The Attempt at a Solution

I assume it was a delta initial condition then apply the kernel. However I need to turn the entropy definition into an integral over space. The kernel times differential volume is the probability finding the particle in that space but the natural log term is tricky.

 

[simoncks]

In short, I would like to know if there are any entropy equation integrating over space.

 

[bjnartowt]

You are asking what entropy S is produced by time t by diffusion through a medium characterized by diffusion coefficient D_{ij}? If so, could you indicate the arrangement of the system at t = 0; is a point-source diffusing?

 

[simoncks]

It is a heat equation without source term. Open boundary at infinity. Initial condition is a delta function at (x,y,z) = 0.