# Entropy of diffusion

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1. Oct 31, 2016

### simoncks

1. The problem statement, all variables and given/known data
The problem requires me to find the entropy of a diffusion constant as a function of time (I guess in terms of diffusion coefficient)

2. Relevant equations
Perhaps Heat / Diffusion kernel
S = k p lnp

3. 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.

2. Nov 5, 2016

### Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Nov 6, 2016

### simoncks

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

4. Nov 6, 2016

### 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?

5. Nov 7, 2016

### simoncks

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