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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