Re: Ludwig Boltzmann, entropy

Tim Tyler <tim@xxxxxxxxxxx> wrote:
>Paul J Gans <gans@xxxxxxxxx> wrote or quoted:
>> Tim Tyler <tim@xxxxxxxxxxx> wrote:
>> >Paul J Gans <gans@xxxxxxxxx> wrote or quoted:
>> >> Tim Tyler <tim@xxxxxxxxxxx> wrote:
>> >> >Paul J Gans <gans@xxxxxxxxx> wrote or quoted:
>> >> >> Tim Tyler <tim@xxxxxxxxxxx> wrote:

>> >> >> >We *still* don't know how many microstates there are in any physical
>> >> >> >system today. Consequently, we still don't know how enormous the
>> >> >> >number of microstates is. Indeed, we don't even know for sure whether
>> >> >> >the number is finite.
>> >> >>
>> >> >> Of *course* we know the number of microstates in a physical
>> >> >> system.
>> >> >>
>> >> >> All one has to do is recognize that W in the formula
>> >> >>
>> >> >> S = k ln W
>> >> >>
>> >> >> is the number of microstates in a system, k is Boltzmann's
>> >> >> constant, and S is the entropy.
>> >> >>
>> >> >> Look up the entropy for a substance (entropies can be measured)
>> >> >> and calculate W from it.
>> >>
>> >> >No - we don't know the entropy of anything either. All we have is
>> >> >crude thermodynamic estimates of it - which might well prove to be
>> >> >completely wrong.
>> >>
>> >> >We *really* don't know the number of microstates in any region of the
>> >> >universe. The information content in any region of space it not known.
>> >>
>> >> >Scientists don't even have an upper bound on the value :-(
>> >>
>> >> At this point I have no idea what you are talking about.
>> >> Entropies are known to three, four, and in some cases
>> >> five significant figures. And those numbers won't prove
>> >> completely wrong.
>> >>
>> >> Given this, W is certainly calculable.
>> >>
>> >> If you are trying to make a non-obvious point, well,
>> >> it is non-obvious to me.
>> >>
>> >> By the way, "information" in general has nothing to
>> >> do with this.
>>
>> >Entropy - according to Boltzmann - is a measure of the disorder
>> >in the system.
>>
>> >If you don't know what information there is in a system, you
>> >can't calculate how disordered. it is.
>>
>> >Thermodynamic entropies may well prove to be totally inaccurate
>> >as measures of the real entropy of systems. They could be
>> >out by orders of magnitudes - not just by a few significant
>> >figures. For example, they completely ignore the possibility
>> >of there being significant entropy within atoms.
>>
>> I'm afraid that you will have to explain what information
>> has to do with any of this.

>Fortunately, others have done that for me - e.g. see the page starting:

>``Entropy is a concept in thermodynamics (see thermodynamic entropy),
> statistical mechanics and information theory. The concepts of
> information and entropy have deep links with one another, although it
> took many years for the development of the theories of statistical
> mechanics and information theory to make this apparent. [...]''

> - http://en.wikipedia.org/wiki/Information_entropy

Whatever.

Look, there certainly are links. I've never denied that.
But I'd not look to a Wiki for complete information.


>> What I suspect, but do not know, is that you are mixing
>> in a bunch of notions from information theory. Don't do
>> that. While the equations look the same and indeed the
>> subjects have a relationship (but not a close one) you
>> simply can't carry all ideas from one over to the other.

>Entropy is *fundamentally* an information-theoretic notion.

NO. Some information theorists claim this, but it is false.

>Historically, the theromdynamic definition of entropy came first -

No kidding.

>but subsequent developments in statistical mechanics and information
>theory revealed that thermodynamic entropy is basically a special
>case of the more general information-theoretic concept.

So?

>Things
>like the second law are really statistical in nature - pure
>information-theory constructs.

This is wrong. And silly. Not everything that is statistical
in nature is information theory. Boltzmann knew it was statistical.
It was even called "statistical mechanics". And the statistical
nature of the second law was shown by Boltzmann, but assumed by
anyone who knew about chemical kinetics and equilibrium.

>It was Boltzmann's contribution started these ideas off originally.

Wow! I'm glad you told me that.

I still want to know why you think the entropy of, for
example, a 12-gram diamond at 1 atm pressure and say 25
degrees C is unknown and unknowable.

---- Paul J. Gans

.

Relevant Pages

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