Re: [Fis] High or low symmetry

Today is clearly a disagreement day :):):). Nevermind...

1. In fact what you are trying to formulate is a well-known principle from
statistical physics that the equilibrium state possesses the highest
symmetry possible. This is a natural consequence of the theorem of
equidistribution of energy between the degrees of freedom. This is not
stability or instability (which possess slightly different meanings). This
result is known to physicists for at least 50-70 years. It also holds for
economics, biology and many other situations, and I think there are tons of
papers about it.

2. Crystal is MORE ORDERED but LESS SYMMETRIC. By definition, symmetry
measures, in very kitchen-physics terms, how many transformations leave the
system unchanged. In homogeneous system any translation at ANY distance does
not change the system whilst in the case of a crystal only those
translations that are integer multiples of the elementary cell size leave
the system unchanged. That is why crystal is less symmetric. This is also
not of my invention, but has been terminologically and ideologically sorted
out about the same time ago. Again, ORDER is different from SYMMETRY, and
often the more ORDERED system is the less SYMMETRIC it is (within, of
course, the framework of commonly accepted definitions of symmetry)

Thanks, Igor

----- Original Message -----
From: "Dr. Shu-Kun Lin" <lin@mdpi.org>
Cc: "Igor Rojdestvenski (by way of Pedro C. Mariju�n )
<igor.rojdestvenski@plantphys.umu.se>" <marijuan@posta.unizar.es>;
"fis-listas.unizar.es" <fis@listas.unizar.es>
Sent: Tuesday, July 22, 2003 2:42 PM
Subject: Re: [Fis] High or low symmetry

> Dear Igor,
>
> How about two kinds of symmetries:
> 1. dynamic symmetries (isotropicity and homogeneity of fluid or spins
above Curie temperature)) and
> 2. static symmetries (crystal certainly has higher static symmetry than
noncrystal, such as
> translational symmetry, or spin parallel configuration below Curie
temperature).
>
> The symmetry principle holds when ALL the other conditions the SAME, the
higher the symmetry
> the higher the stability. For barometric formula, at the same altitude the
most stable distribution must be
> the homogeneous one (If Florida has a low pressure and the ocean has
higher pressure
> there will big wind, the process to become the same pressure on the same
altitude).
>
> Shu-Kun
>
> "Igor Rojdestvenski (by way of "Pedro C. Mariju�n" )" wrote:
>
> > Dear Dr. Shu-Kun Lin,
> >
> >
> > I am still not convinced. Take the dewpoint example. At high
temperatures water vapour is symmetrically (i.e. homogeneously and
isotropically) mixed
> > into the air. At other temperatures the stable state, i.e. the state the
system equilibrates into, is a state of lower symmetry with droplet
> > nucleation, growth and droplet size distribution equilibration. Hence,
we cannot UNIVERSALLY say that more symmetry means more stability. At high
> > temperatures you are probably right, but not at ALL temperatures.
> >
> > Another example is a magnetic lattice with each lattice site having spin
either up or down (so called Ising model). Again, above the Curie point the
> > isotropic and homogeneous state is more stable, and the fluctuations
occurring in this state decay. Below Curie point, however, the more stable
> > state is the one with lower symmetry (a preferred direction occurs).
Again, the fluctuations from this state decay. This is kind of commonplace
in
> > the theory of phase transitions and critical phenomena, good reading
about it is still Stanley's book "Phase transitions and critical phenomena".
> >
> >
> > And crystal is, in fact, LESS symmetric than non-crystalline state, both
microscopically and macroscopically. It has selected directions (axes of
> > elementary cell), hence it is not isotropic. The disordered state
(liquid) is typically isotropic, except for the cases like liquid crystals.
> >
> > This is easy to understand in terms of the co-called phase space, or the
space in which the system's microscopic states occupy a certain area. Very
> > simplistically, the smaller is the area, the less symmetric is the
system, as the more limitations to the possible states occur. The phase
space for
> > a crystal is smaller than for a disordered system.
> >
> > As to your homogeneous gas example, we are mixing two things here. If we
talk equilibrium states, then in equilibrium (and in the absense of
> > external fields) gas is typically homogeneous and isotropic. If external
fields apply (i.e. gravity), we have stable inhomogeneous state in the form
> > of barometric formula. And this state is more stable (in the gravity
field) than the homogeneous, equidense one.
> >
> > Regards, Igor
> > Dr. Igor Rojdestvenski,
> > Dept. Plant Physiology,
> > Umea university,
> > Umea 90187,
> > Sweden
> > e-mail: igor.rojdestvenski@plantphys.umu.se
> > phone: +46-73-6205020
> > fax: +46-90-7866676
> > homepage: www.patronov.net
>
> --
> Dr. Shu-Kun Lin
> Molecular Diversity Preservation International (MDPI)
> Matthaeusstrasse 11, CH-4057 Basel, Switzerland
> Tel. +41 79 322 3379, Fax +41 61 302 8918
> e-mail: lin@mdpi.org
> http://www.mdpi.org/lin
>
>
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Received on Tue Jul 22 16:21:26 2003