Hey everyone. Thanks to github sites, and netlify. This blog is available at jparkhill.github.io, or www.bbgky.net. Can you believe that domain wasn’t taken? It’s wild!
For those unfamiliar BBGKY (Bogoliubov–Born–Green–Kirkwood–Yvon) is a name given in many different contexts (classical and quantum mechanics and finance) to equations of motion for probabilities. BBGKY casts the equations of motion into a form where n-degree of freedom effects are partitioned into a hierarchy.
The BBGKY hierarchy one of those inevitable ideas which will occur in many contexts under many different names. It’s closely related to the idea of a ‘signature transformation’ in the statistics of signals, or cluster expansion in the theory of correlated scattering.
In quantum mechanics, BBGKY formally rewrites the N-particle quantum Liouville equation (which is linear and therefore well understood, mathematically but numerically intractable) as coupled nonlinear partial differential equations (which are tractable but not really understood at all, mathematically!).