The Overlapping distribution method was introduced by Charles H. Bennett for estimating chemical potential.
Theory
For two N particle systems 0 and 1 with partition function and ,
from
get the thermodynamic free energy difference is
For every configuration visited during this sampling of system 1 we can compute the potential energy U as a function of the configuration space, and the potential energy difference is
Now construct a probability density of the potential energy from the above equation:
where in is a configurational part of a partition function
since
now define two functions:
thus that
and can be obtained by fitting and
References