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Overlapping distribution method : ウィキペディア英語版
Overlapping distribution method

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 Q_ and Q_ ,
from F(N,V,T) = - k_T \ln Q
get the thermodynamic free energy difference is \Delta F = -k_T \ln (Q_/Q_) = - k_ T \ln (\frac(s^) )}(s^) )})
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
\Delta U = U_(s^) - U_(s^)
Now construct a probability density of the potential energy from the above equation:
p_(\Delta U) = \frac)\delta(U_-U_-\Delta U)} is a configurational part of a partition function

p_(\Delta U) = \frac)\delta(U_-U_-\Delta U)}\exp(U) )\delta(U_-U_-\Delta U)}}\exp(-\beta U_)\delta(U_-U_-\Delta U)}}(\Delta U)

since
\Delta F = -k_T \ln (Q_/Q_)
\ln p_(\Delta U) = \beta(\Delta F -\Delta U) + \ln p_(\Delta U)
now define two functions:
f_(\Delta U) = \ln p_(\Delta U) - \frac
f_(\Delta U) = \ln p_(\Delta U) + \frac

thus that
f_(\Delta U) = f_(\Delta U) + \beta\Delta F
and \Delta F can be obtained by fitting f_ and f_

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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