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 formula_1 and formula_2 , 
from formula_3
get the thermodynamic free energy difference is formula_4
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 
formula_5
Now construct a probability density of the potential energy from the above equation:
formula_6
where in formula_7 is a configurational part of a partition function
formula_8 
formula_9
since 
formula_10
formula_11
now define two functions:
formula_12
thus that 
formula_13
andformula_14 can be obtained by fitting formula_15 and formula_16
References.
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