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On the density of volume states in the isobaric ensemble Phil Attard
 

Summary: NOTES
On the density of volume states in the isobaric ensemble
Phil Attard
Department of Physics, Faculty of Science, Australian National University, Canberra, ACT, 0200, Australia
Received 14 June 1995; accepted 10 August 1995
The Gibbs or information entropy, S kB i i ln i , in
the continuum limit becomes1
S kB dx x x ln x , 1
where (x) is the density of states, (x) is the probability of
one particular state, and (x) (x) (x) is the probability
density, i.e., x) dx is the probability of finding the system
between x and x dx]. The density of states is essential for
the entropy to be invariant under coordinate transformations,
i.e., for y y(x), y(y) dy (x)dx . Given some average
quantity f(x) , the maximum entropy principle yields the
probability density1
x Z 1
e f x
x , 2
where the partition function is

  

Source: Attard, Phil - School of Chemistry, University of Sydney

 

Collections: Chemistry