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

L= N log x is the expression in general, where N is the
the size of a sample. Excuse me.

Shu-Kun

Dr. Shu-Kun Lin wrote:

> 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/
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