Re: [Fis] Replies and new questions / part 1

Dear Michel,

> About the relations entropy/order-disorder/symmetry, mentioned by Shu-Kun Lin:
> I had in the past several discussions with Shu-Kun about this topic.
> It appeared that order/disorder is a paradoxical concept, which is
> not very clear. Here is an simple example, based upon samples of the
> uniform law in a square. N being the size of a sample, my question is:
> does order decreases and disorder increases when N increases, or
> does order increases and disorder decreases when N increases ?
> I shall give my own view in a future email.
> The same question for entropy or information may be easier to answer,
> because we are in a strictly probabilistic context.

If order (nonsymmetry) is represented by information I, disorder (symmetry)
by entropy S, you are talking about I/N and S/N or about additivity or extensivity.
For convenience, let us put L=I+S. If the structure is not changed, I/S will not change
if only N increases. This means I and S will increase or decrease together.

In computer, for a memory solid device (a hard disk or a floppy disk) the
number of variable x is fixed, it is of course additive (N becomes
2N, I becomes 2I). For example, x =(0,1) or x=2. I/N=log2 is a constant for
a system recorded information where further compression (zip) is impossible.

In many cased, additivity does not hold true. For example, if we assess the biodiversity
of microorganism. Among the 1000000 samples (N=1000000) we found a new bacteria.
Its information is I=log1000000 per sample for this sample. This means we
calculate the maximum information (Its symbol has been put as L, L=I+S)
as L= x log N = N log N, where the variable x=N.

One more case is the number of permutation (transformation by exchanging N chairs
in a meeting rooms of N people), L=log (N!), where N! of course is N (N-1) ... 4.3.2.1.
This term log (N!) has been argued for more than 100 years in the so-called Gibbs
Paradox of entropy of mixing. For such systems of ideal gas, it cannot lead to
any clear conclusion about its additivity if the argument is about this one system.
To me, the variable is x=N! when permutation is considered and the real N (let us
use n, the size of a sample) is 1. If there is an array of n such systems, L=n log (N!)
and additivity will be followed: n becomes 2n, L will become 2L.

> About the thermodynamic equilibrium and the universe, in the reply of Stan Salthe:
> Since cosmology is far from my field, I confess to have difficulties to
> understand the properties of the system <<our universe>>, viewed from the
> thermodynamical viewpoint. Even the cooling of such an expanding system
> is not clear for me, since, despite that the expansion is (locally) currently
> observed, I do not know what will happen after some 1O10 years or more
> (does anybody knows ?), and may be there are cycles, may be there are
> aperiodic contractions, may be there is...anything. I would like to
> hear further opinions about this.

Universe = system + environment. Universe is divided to 2 parts.
We consider the system carefully and its surroundings (environment)
not really carefully.

Thanks!

(Michel asked me to send this message to the whole FIS list)

Shu-Kun

-- 
Dr. Shu-Kun Lin
Molecular Diversity Preservation International (MDPI)
Matthaeusstrasse 11, CH-4057 Basel, Switzerland
Tel. +41 61 683 7734 (office)
Tel. +41 79 322 3379 (mobile)
Fax +41 61 302 8918
E-mail: lin@mdpi.org
http://www.mdpi.org/lin/
_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis