Re: Ludwig Boltzmann, entropy

On Sat, 6 Aug 2005 02:42:09 +0000 (UTC), Paul J Gans <gans@xxxxxxxxx>
wrote:

>Tim Tyler <tim@xxxxxxxxxxx> wrote:
>>Paul J Gans <gans@xxxxxxxxx> wrote or quoted:
>>> Tim Tyler <tim@xxxxxxxxxxx> wrote:
>>> >rnorman <rnorman@xxxxxxxxx> wrote or quoted:
>
>>> >> The fact is, information in the Shannon sense is most definitely a
>>> >> notion closely related in formulation to the statistical dynamical
>>> >> notion of entropy as a measure of a subset of states. Tim Tyler is
>>> >> sort of partially on the right track. Paul Gans is correct, though.
>>> >> It is NOT true that entropy is an information-theoretic notion. I
>>> >> don't believe any information theorist really claims this.
>>>
>>> >Entropy *is* in information theoretic notion. It is just not
>>> >*only* an information theoretic notion.
>>>
>>> >Where it's important to distinguish between the terms, people use
>>> >terms like "information entropy" and "thermodynamic entropy".
>>>
>>> >The distinction is pretty irrelevant to this thread, though.
>>>
>>> >The discussion started with the question of whether the number of
>>> >microstates in physical systems was known. They are not known for any
>>> >physical system - unless you adopt a notion of microstates tht bundles
>>> >similar velocities together, and call them indistinguishable - and if
>>> >you do that there's no generally agreed-upon framework that dictates
>>> >what granularity of "bucket" you can use - and different size buckets
>>> >produce different results for the number of microstates involved.
>>>
>>> I'm sorry but this is wrong. And has been known to be wrong
>>> since about 1910. That was the period in which Sakur and
>>> Tetrode worked out the size of a microstate. It turned out
>>> to be Planck's constant to the third power.
>>>
>>> With the development of quantum mechanics and the Heisenberg
>>> uncertainty principle came an understanding of *why* that
>>> was the size of a microstate.
>
>>Microstates don't have a size. They are configurations.
>>Classically, each microstate of a system is a statement about
>>the position, momentum and nature of particles in the system.
>
>>> This isn't just speculation. That's the number you need
>>> to use in the appropriate equations to calculate the entropy.
>>> And that entropy agrees with experiment.
>>>
>>> Got it?
>
>>No. There may be more states than you claim - or fewer states.
>
>>HUP doesn't place a limit on the number of states the universe
>>can take, it's a limit on what knowledge embedded observers
>>can obtain about that state - a different concept.
>
>>The entropies calculatied using Boltzmann's constant from thermodynamic
>>parameters are based on hypotheses about the particulate nature of
>>matter, the lack of other properites apart from positon and velocity,
>>the assumption that all the relevant particles are known about, and
>>speculation about the granularity of the universe. The results from
>>this model may be interesting - but they should not be mistaken for
>>what's going on in the real world in any volume of spacetime.
>
>Well, we'll have to agree to differ. But you might
>read a book or two on thermodynamics, statistical
>mechanics, and quantum mechanics.
>

The whole subject of thermodynamics seems to be an example of what
Laughlin describes as a systems emergent property, much like the ideal
gas law which is in fact at the heart of thermo. As Laughlin
describes it ("A Different Universe: Reinventing Physics from the
Bottom Down", Basic Books, 2005) the fact that the original
derivation of the gas law was based on totally flawed notions of what
atoms are and how they behave is entirely irrelevant. As soon as you
move far enough into the ensemble to no longer see the individual
particles the system takes over and the theory becomes valid. In
other words, the system level thermodynamics, whether from the
macroscopic phenomenological perspective or from the statistical
ensemble perspective (as long as you average over sufficient
particles), are rather insensitive of the details of what the
individual particles do.





.

Relevant Pages

  • Thermodynamics and the Universe.
    ... Thermodynamics and the Universe. ... In 1850 Rudolph Clausius formulated the Second law of thermodynamics: ... "The theory in which thermal qualities of the particles without ...
    (sci.physics.relativity)
  • Re: Challenging exercises in relativity theory
    ... I think exercise 3 is the easiest, ... Would the result suggest that the universe is ... Assume that you have n particles of mass m and the momentum of the nth ... then a sphere of volume V will enclose the mass density rho_0*V. ...
    (sci.physics.relativity)
  • Re: On Higher Dimensional Travel
    ... If we ever find an intelligent civilization elsewhere in the universe, ... When you factor in the light travel time, one would have to wait 200 ... For example, gravitons, the theoretical particles that carry the gravitational ... Petit and Sarrazin describe a less well-studied scenario where the two branes ...
    (soc.retirement)
  • On Higher Dimensional Travel
    ... If we ever find an intelligent civilization elsewhere in the universe, ... When you factor in the light travel time, one would have to wait 200 ... For example, gravitons, the theoretical particles that carry the gravitational ... distances there may be shorter than in our own brane. ...
    (soc.retirement)
  • Re: Lecture: Dark Mater
    ... So, the universe is expanding and dark matter, ... conservation of energy since...we're dealing with quantum particles. ... Any two such plates anywhere in the universe no matter ... More correctly, there is an infinite ...
    (talk.origins)
Loading