A few additional comments relating to our discussion earlier today
about rate theories and what you might look for in comparing them:

1. Watch for the averaging...

Whenever one goes from a microscopic description, such as a
Newton's-Laws description at the level of atoms or molecules, to a
macroscopic description, such as one at the level of experiment, there
must be statistical averaging:  we do not know enough to solve a
microscopic model; and we want to end up with a description of only one
or a small number of macroscopic variables - for a rate process,
typically a rate constant.

The averaging for a classical system is performed as an integration
over phase space for some quantity or quantities that can be tied
perhaps to a macroscopic description.  For example, a partition
function, a projection operator, a reaction coordinate, etc.


2. Watch for averaging implicit or hidden in some feature of the model...

The Langevin equation of motion used to describe the dynamics of
diffusion; the Mori-Zwanzig formalism and the Generalized Langevin
equation; a reaction coordinate; projection and projection operators;

Averaging can be at more than one stage of the analysis, e.g., when
features like the above are present in the model.


3. Watch for tricks...

In the averaging, the theoretician often has had to be clever and
possibly has used tricks or restrictive assumptions to obtain a
solution to the mathematical expression of the model.


4. Watch for the time scales...

The averaging may require assumptions about time scales for some or
many or most of the microscopic variables.


5. Watch for the method of handling interactions between variables...

How does a theory incorporate interaction between a variable tied to
the macroscopic description, e.g., the reaction coordinate, and the
other variables of the system?