Inner product structure for classical diff equations

[julian]

I'm interested in what people know about the application of inner product structures (usually reserved for QM) to diff equations describing classical physics, in particular non- hermitician diff operator of the Fokker-Plank equation. Thanks.

 

[Stephen Tashi]

Before your thread gets the automated courtesy bump, let me suggest you explain what you mean by an "inner product structure". Do you mean a vector space of functions with an inner product?

 

[julian]

Before your thread gets the automated courtesy bump, let me suggest you explain what you mean by an "inner product structure". Do you mean a vector space of functions with an inner product?

Yes. I've found this:

http://wwwf.imperial.ac.uk/~pavl/lec_fokker_planck.pdf

and I'm looking at it now, but it only applies to where you have gradient flows (that's where the diffusing particle is also subject to steady state flow given by the grad of a potential) and the operator is hermitician.