How does maximum symmetry compare to its corresponding minimum symmetry?

[Loren Booda]

In a mathematical system, what similarities are there between the most and least absolute symmetries?

Might Noether's theorem explain this?

 

[HallsofIvy]

Before anyone can answer this, you will need to specify what you mean by "maximum" and "minimum" symmetry. How are you ordering symmetries?

 

[Loren Booda]

I was thinking in part of "maximum" temperatures and "minimum" temperatures, as considered with a magnetic field -- are they of equal symmetry?

 

[Loren Booda]

I was thinking in part of "maximum" temperatures and "minimum" temperatures, as considered with a magnetic field -- are they of equal symmetry?

Make that temperature "approaching infinity" and temperature "approaching negative infinity."

 

[HallsofIvy]

You do understand "absolute zero" do you not?

But, in what sense does a mathematical system have a "temperature"?

 

[Loren Booda]

I believe I once saw in Scientific American the concept of negative temperature relative to "absolute" zero. The system discussed was of a theoretical magnetic field that represented a temperature approaching infinity, but in a similar symmetric configuration could (ironically) represent temperature approaching negative infinity.