v. guruprasad
Nov19-04, 01:26 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>> v. guruprasad wrote:\n>\n> > The correct restatement of Lemma 1 should be that the *information\n\nI\'ve corrected the manuscript, throwing away Lemma 1, which I really\ndidn\'t need but for the notational convenience!! We do need the theorem\nthat followed it, mainly to identify the half-wavelength intervals that\nI\'m evidently fixated on, so it\'s now gone to the appendix.\n\n[I apologize for not correcting it right away - all of my "spare time"\nlast week was tied up with the effort of putting up an "outlandish\ntheoretical products" exhibit at Nano2004!]\n\n\nGerard Westendorp <westy31@xs4all.nl> wrote in message news:<41993E2E.8080006@xs4all.nl>...\n> One point I do not like is the argument that a finite system\n> can never thermalize because we can know it completely, and\n> therefor it has zero entropy. I think this is a bit beside\n> the point. If Fermi, Pasta and Ulam had used a different\n> equation, one with less symmetries, they would have\n> obtained an energy distribution that would be pretty much flat.\n\nThat has been the expectation starting with FPU themselves. However,\nmany bright people have clearly been working on it, and I\'d think\nwould have presumably applied as many different equations as they\npossibly could by now.\n\nThe fact that the expectation isn\'t achieved yet could mean it\'s\nimpossible, just as much as that success could be just around the\ncorner. The simulations themselves are thus inconclusive.\n\nAs better explained in Section I of the revised version, the\nLandauer-Bennett Maxwell demon theory leads to a definitive answer\nthat the expectation has been fundamentally mistaken all along.\n\nHowever, as also explained better in the revision, my derivation\ndoes not really depend on this answer.\n\n\n> The fact that it is known completely is too\n> philosophical; what matters is that it can serve as a good\n> approximation of something incompletely known.\n\nIt\'s not about knowledge but its representation. You need a number of bits\nof physical storage to simulate a system. There\'s no way to physically\nrepresent any variable with infinite precision, nor even infinite\nnumber of variables with finite precision. So the total number of bits\nin any real computation is finite. As long as you have a finite number\nof bits to model with, and all operations are deterministically defined\nover collections of those bits, the best you can get from the simulation\nis a pseudo-random sequence with eventually repeats. The only known way of\nmaking it totally random is to introduce hardware-generated noise, but\nthat *is* coupling to the ambient thermal motions, not simulation!\n\n\n\n> However, this need not spoil everything yet. A proper\n> "FPU" experiment should also contain some sort of observer,\n> and this observer needs to receive chunks of kT for\n> each fact that he knows. Again, I\'ll need to think\n> a bit about this.\n\nJust remember that the kT/2 chunks can be received from a power supply\n(see Fig. 4). (You\'re welcome to get your own kT/2\'s by thinking!)\n\n\nIn any case, as I\'ve just said, the FPU issue is secondary. I only use\nit to claim that my derivation stands up to a stronger constraint than\npresent notions. Conversely, I\'m implying the current premises, e.g.\nof quantum statistical mechanics and of the second quantization\nformalism of bosons or fermions, are incomplete and do not suffice\nfor assuming thermalization.\n\n\n\n> > is the reduction of entanglement - which does not even depend on\n> > Planck\'s law or h at all, and should appear all too easy.\n>\n> I\'ll be reading it.\n\nI so greatly appreciate it!\n\n\nthanks,\n-prasad\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>> v. guruprasad wrote:
>
> > The correct restatement of Lemma 1 should be that the *information
I've corrected the manuscript, throwing away Lemma 1, which I really
didn't need but for the notational convenience!! We do need the theorem
that followed it, mainly to identify the half-wavelength intervals that
I'm evidently fixated on, so it's now gone to the appendix.
[I apologize for not correcting it right away - all of my "spare time"
last week was tied up with the effort of putting up an "outlandish
theoretical products" exhibit at Nano2004!]
Gerard Westendorp <westy31@xs4all.nl> wrote in message news:<41993E2E.8080006@xs4all.nl>...
> One point I do not like is the argument that a finite system
> can never thermalize because we can know it completely, and
> therefor it has zero entropy. I think this is a bit beside
> the point. If Fermi, Pasta and Ulam had used a different
> equation, one with less symmetries, they would have
> obtained an energy distribution that would be pretty much flat.
That has been the expectation starting with FPU themselves. However,
many bright people have clearly been working on it, and I'd think
would have presumably applied as many different equations as they
possibly could by now.
The fact that the expectation isn't achieved yet could mean it's
impossible, just as much as that success could be just around the
corner. The simulations themselves are thus inconclusive.
As better explained in Section I of the revised version, the
Landauer-Bennett Maxwell demon theory leads to a definitive answer
that the expectation has been fundamentally mistaken all along.
However, as also explained better in the revision, my derivation
does not really depend on this answer.
> The fact that it is known completely is too
> philosophical; what matters is that it can serve as a good
> approximation of something incompletely known.
It's not about knowledge but its representation. You need a number of bits
of physical storage to simulate a system. There's no way to physically
represent any variable with infinite precision, nor even infinite
number of variables with finite precision. So the total number of bits
in any real computation is finite. As long as you have a finite number
of bits to model with, and all operations are deterministically defined
over collections of those bits, the best you can get from the simulation
is a pseudo-random sequence with eventually repeats. The only known way of
making it totally random is to introduce hardware-generated noise, but
that *is* coupling to the ambient thermal motions, not simulation!
> However, this need not spoil everything yet. A proper
> "FPU" experiment should also contain some sort of observer,
> and this observer needs to receive chunks of kT for
> each fact that he knows. Again, I'll need to think
> a bit about this.
Just remember that the kT/2 chunks can be received from a power supply
(see Fig. 4). (You're welcome to get your own kT/2's by thinking!)
In any case, as I've just said, the FPU issue is secondary. I only use
it to claim that my derivation stands up to a stronger constraint than
present notions. Conversely, I'm implying the current premises, e.g.
of quantum statistical mechanics and of the second quantization
formalism of bosons or fermions, are incomplete and do not suffice
for assuming thermalization.
> > is the reduction of entanglement - which does not even depend on
> > Planck's law or h at all, and should appear all too easy.
>
> I'll be reading it.
I so greatly appreciate it!
thanks,
-prasad
>
> > The correct restatement of Lemma 1 should be that the *information
I've corrected the manuscript, throwing away Lemma 1, which I really
didn't need but for the notational convenience!! We do need the theorem
that followed it, mainly to identify the half-wavelength intervals that
I'm evidently fixated on, so it's now gone to the appendix.
[I apologize for not correcting it right away - all of my "spare time"
last week was tied up with the effort of putting up an "outlandish
theoretical products" exhibit at Nano2004!]
Gerard Westendorp <westy31@xs4all.nl> wrote in message news:<41993E2E.8080006@xs4all.nl>...
> One point I do not like is the argument that a finite system
> can never thermalize because we can know it completely, and
> therefor it has zero entropy. I think this is a bit beside
> the point. If Fermi, Pasta and Ulam had used a different
> equation, one with less symmetries, they would have
> obtained an energy distribution that would be pretty much flat.
That has been the expectation starting with FPU themselves. However,
many bright people have clearly been working on it, and I'd think
would have presumably applied as many different equations as they
possibly could by now.
The fact that the expectation isn't achieved yet could mean it's
impossible, just as much as that success could be just around the
corner. The simulations themselves are thus inconclusive.
As better explained in Section I of the revised version, the
Landauer-Bennett Maxwell demon theory leads to a definitive answer
that the expectation has been fundamentally mistaken all along.
However, as also explained better in the revision, my derivation
does not really depend on this answer.
> The fact that it is known completely is too
> philosophical; what matters is that it can serve as a good
> approximation of something incompletely known.
It's not about knowledge but its representation. You need a number of bits
of physical storage to simulate a system. There's no way to physically
represent any variable with infinite precision, nor even infinite
number of variables with finite precision. So the total number of bits
in any real computation is finite. As long as you have a finite number
of bits to model with, and all operations are deterministically defined
over collections of those bits, the best you can get from the simulation
is a pseudo-random sequence with eventually repeats. The only known way of
making it totally random is to introduce hardware-generated noise, but
that *is* coupling to the ambient thermal motions, not simulation!
> However, this need not spoil everything yet. A proper
> "FPU" experiment should also contain some sort of observer,
> and this observer needs to receive chunks of kT for
> each fact that he knows. Again, I'll need to think
> a bit about this.
Just remember that the kT/2 chunks can be received from a power supply
(see Fig. 4). (You're welcome to get your own kT/2's by thinking!)
In any case, as I've just said, the FPU issue is secondary. I only use
it to claim that my derivation stands up to a stronger constraint than
present notions. Conversely, I'm implying the current premises, e.g.
of quantum statistical mechanics and of the second quantization
formalism of bosons or fermions, are incomplete and do not suffice
for assuming thermalization.
> > is the reduction of entanglement - which does not even depend on
> > Planck's law or h at all, and should appear all too easy.
>
> I'll be reading it.
I so greatly appreciate it!
thanks,
-prasad