http://friam.383.s1.nabble.com/Definition-of-Complexity-tp522229p522266.html
spacetime limit. As for string theory (or whatever), I think the grand
But I don't think this is being overly broad. Did I
define it. He proposes something called weak emergence, which relates
> OK, I think I'm getting it. It really is down to whether the microlanguage
> is the same as the macrolanguage (no emergence) or different (emergence).
>
> But doesn't that lead to an extraordinarily broad definition of emergence?
> For example, my macrolanguage for describing gravity involves mass and G and
> inverse square laws. But my microlanguage either involves gravitons (if I'm
> a particle physicist) or curved spacetime (if I'm a general relativist). The
> fact that either of these microlanguages give the same results as the
> macrolanguage in the classical limit in no way implies that the micro-and
> macro-languages are the same (exactly as with the micro- and macro-language
> descriptions of entropy). So gravity is emergent.
>
> So if entropy is emergent and gravity is emergent and any other force
> mediated by a subatomic particle is emergent, just how useful is it to label
> something 'emergent' in this way? If the definition of emergence is so
> broad, how can we usefully use it?
>
> Robert
>
>
>
> On 7/24/06, Russell Standish <r.standish at unsw.edu.au> wrote:
> >
> >On Tue, Jul 25, 2006 at 06:46:12PM -0600, Robert Holmes wrote:
> >> >
> >> >
> >> >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
> >
> >You have just written the canonical partition function. This assumes
> >that the universe is divided into two parts, the system, and its
> >environment, and that these are in thermal contact with each other.
> >
> >If you further assume that particles can move between the system and
> >environment, then you get the grand canonical partition function:
> >
> >Z=\sum_{N=0}^{\infty}\sum_{{n_i}}\prod_i exp(-n_i(E_i-\mu)/kT)
> >
> >These assumptions are not microscopic in nature, but how we choose
> >to divide up physical reality. (The choice is needn't be arbitrary - in
> >most stat phys situations, there is a clear "best choice", and choosing
> >any other way of looking at the system is crazy, but you must
> >recognise that it is still a choice independent of microscopic dynamics).
> >
> >Cheers
> >
> >--
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> >
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> >UNSW SYDNEY 2052 R.Standish at unsw.edu.au
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is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
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