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Derivatives of the reduced entropy
Briefly,
where 
is the reduced entropy based on the distribution 
,
a reduction of the full distribution, and 
.
Thus the derivative above is the second order correlation between the logarithm
of the reduced distribution and the energy. In the non-reduced case we
have that 
.
Also,
Note that for a probability distribution that factors, as for independent
particles, as
the reduced entropy is simply the entropy of the subsystem not averaged
over, and 
,
where 
is the energy of the reduced system. All of the previous expressions equations
10.8-
10.19
hold for the subsystem, as expected.
David Wolf
Tue Mar 25 08:11:49 CST 1997