Re: [Fis] High or low symmetry

Thanks for the first point. I put equilibrium as a kind of stability.

Crystal is of course less symmetric than a liquid. However, it
is more symmetric than a noncrystal.

Shu-Kun

Igor Rojdestvenski wrote:

> 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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>
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--
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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