Russell,
> This is circular - temperature is usually defined in terms of
> entropy:
>
> T^{-1} = dS/dE
This is wrong. The temperature is defined according to the Zeroth Law.
The Second Law just allows us to define the absolute temperature, but
the temperature as such is defined independently from the entropy.
>> dependent. As far as I remember, you have used this term in
>> respect to informational capacity of some modern information
>> carrier and its number of physical states. I would suggest to stay
>> with this example as the definition of context dependent.
>> Otherwise, it does not make much sense.
>
> It makes just as much sense with Boltzmann-Gibbs entropy. Unless
> you're saying that is not connected with thermodynamics entropy..
Unfortunately I do not get your point. In the example, with the
information carrier we have different numerical values for the
information capacity on the carrier according to the producer and the
values derived from the thermodynamic entropy.
I still do not understand what surface effects on the carrier has to do
with this difference. Do you mean that if you consider surface effects
you derive an exact equation that will connect the information capacity
of the carrier with the thermodynamic entropy? If yes, could you please
give such an equation?
Evgenii
On 06.02.2012 22:17 Russell Standish said the following:
On Mon, Feb 06, 2012 at 08:36:44PM +0100, Evgenii Rudnyi wrote:
On 05.02.2012 23:05 Russell Standish said the following:
The context is there - you will just have to look for it. I
rather suspect that use of these tables refers to homogenous bulk
samples of the material, in thermal equilibrium with a heat bath
at some given temperature.
I do not get your point. Do you mean that sometimes the surface
effects could be important? Every thermodynamicist know this.
However I do not understand your problem. The thermodynamics of
surface phenomena is well established and to work with it you need
to extend the JANAF Tables with other tables. What is the problem?
The entropy will depend on what surface effect you consider
significant. Is it significant that the surface's boundary bumps an
dimples are so arranged to spell out a message in English? What if
you happen to not speak English, but only Chinese? Or might they not
be significant at all? All of these are different contexts.
Ignoring surface effects altogether is a perfectly viable model of
the physical system. Whether this is useful or not is going to
depend, well, on the context.
It would be good if you define better what do you mean by context
dependent. As far as I remember, you have used this term in
respect to informational capacity of some modern information
carrier and its number of physical states. I would suggest to stay
with this example as the definition of context dependent.
Otherwise, it does not make much sense.
It makes just as much sense with Boltzmann-Gibbs entropy. Unless
you're saying that is not connected with thermodynamics entropy...
If we were to take you at face value, we would have to conclude
that entropy is ill-defined in nonequlibrium systems.
The entropy is well-defined for a nonequilibrium system as soon as
one can use local temperature. There are some rare occasions where
local temperature is ambiguous, for example in plasma where one
defines different temperatures for electrons and molecules. Yet,
the two temperatures being defined, the entropy becomes again
well-defined.
This is circular - temperature is usually defined in terms of
entropy:
T^{-1} = dS/dE
More to the point - consider milling whatever material you have
chosen into small particles. Then consider what happens to a
container of the stuff in the Earth's gravity well, compared with
the microgravity situation on the ISS. In the former, the stuff
forms a pile on the bottom of the container - in the latter, the
stuff will be more or less uniformly distributed throughout the
containers volume. In the former case, shaking the container will
flatten the pile - but at all stages the material is in thermal
equilibrium.
In your "thermodynamic context", the entropy is the same
throughout.
No it is not. As I have mentioned in this case one just must
consider surface effects.
Hence the context.
It only depends on bulk material properties, and temperature.
But most physicists would say that the milled material is in a
higher entropy state in microgravity, and that shaking the pile
in Earth's gravity raises the entropy.
Furthermore, lets assume that the particles are milled in the
form of tiny "Penrose replicators" (named after Lionel Penrose,
Roger's dad). When shaken, these particles stick together,
forming quite specific structures that replicate, entraining all
the replicators in the material.
(http://docs.huihoo.com/reprap/Revolutionary.pdf).
Most physicists would say that shaking a container of Penrose
replicators actually reduces the system's entropy. Yet, the
thermodynamic entropy of the JNAF context does not change, as
that only depends on bulk material properties.
We are again at the definition of context dependent. What are
saying now is that when you have new physical effects, it is
necessary to take them into account. What it has to do with your
example when information on an information carrier was context
dependent?
Who decides what physical effects to take into account? This is not
a question of pure relativism - I'm well aware that some models are
much better than others at describing the situtaion, but even in the
case of Penrose replicators described above, their ability to adhere
and fragment may or may not be relevant to the situation you are
trying to model.
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