[FRIAM] Definition of Complexity

[Phil Henshaw]

perhaps because it's a sum?
 
 

Phil Henshaw                       ¸¸¸¸.·´ ¯ `·.¸¸¸¸
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-----Original Message-----
From: friam-bounces at redfish.com [mailto:friam-bounces at redfish.com] On
Behalf Of Robert Holmes
Sent: Tuesday, July 25, 2006 8:46 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Definition of Complexity




One can certainly start from the partition function. But the partition
function is something that is additional to the microscopic 
description, hence emergent. Indeed, the partition function is
different depending on whether you are using microcanonical, canonical
or grand canonical ensembles, each of which is a thermodynamic, not
microscopic concept. 


I'm surprised that you consider the partition function as being "in
addition" to the microscopic description. Is this the common view in
statistical mechanics? Just to be specific, if I've got a system of
distinguishable particles and the energy levels aren't degenerate, the
single particle partition function Zsp is given by: 


Zsp = sum( exp( -ei/k.T ) )

where ei is the energy of the energy level i, the sum is over all i
(i.e. over all energy levels), k is the Boltzmann constant and T is the
temperature. 
 
Now that seems about as microscopic description of a system as you can
get. Could you explain why it's not please?

Thanks for your patience!

Robert 



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