I think that a jump in the first derivatives would be way too manifest. For example, if the stock market goes down and suddenly it starts to go up, you will notice. The
same thing holds for other bubbles? sizes in physics, too.

Second derivatives of course – that’s what I meant. Sometimes my fingers (and neurons) do mis-shoot, probably, because I want to focus on too many things simultaneously

For example, if bubbles grow uniformly, linearly and suddenly they start to grow exponentially, you may also notice, although it?s harder.

Second order phase transition is supposed to be completely smooth, the growth of bubbles of the new phase only takes place for a first order phase transition.

I tend to think that even this is possible.

As follows from your previous comment, you actually tend to think that it is possible to notice the jump in derivatives higher than 2nd, which seems quite unlikely to me.

Appreciated your stock market irony
Cheers,

I think that a jump in the first derivatives would be way too manifest. For example, if the stock market goes down and suddenly it starts to go up, you will notice. The same thing holds for other bubbles’ sizes in physics, too.

But a continuous free energy and a discontinuous first derivative is not what defines the second order phase transition: it is exactly a definition of the first order phase transition.

Whether the second order phase transition is visible is a question whether you can “see” the jump in the second derivatives of the thermodynamic potentials, and I tend to think that even this is possible. For example, if bubbles grow uniformly, linearly and suddenly they start to grow exponentially, you may also notice, although it’s harder.

Best
Lubos

theoreticalminimum: It looks like supercritical carbon dioxide undergoing phase transition to a gas-liquid mixture.

Indeed so. I wonder how you were able to recognize that this is CO2 I have honestly decided not to read the description of the video and thought all the way that this is water near the critical point

Lubos: I don’t want to be picky but the English term for the “second kind” phase transitions are “second order phase transition”.

Thank you for being picky. Everything is corrected (in the previous post as well). I have no idea why I used this particular wording.

Lubos: And I don’t want you to panic

It is not like I am in panic. Actually, I am petrified and shaken.

Lubos: the transition from the liquid-like to gas-like supercritical CO2 is actually a higher-order phase transition

Thanks for the link! I did not know that. Actually, if I would also want to be picky, I would say that “higher-order phase transition” staff belongs to old classification by Ehrenfest, there are only first and second order phase transitions nowadays: the former involve latent heat, the latter – don’t; correlation length is finite for the former and goes to infinity for the latter.

Lubos: which might even be somewhat manifest in the video you included because the video is damn continuous and smooth, isn’t it?

Well, for the second order PT thermodynamic potentials change smoothly, and I don’t think one would be able to notice a jump in first derivatives.

Cheers,

I don’t want to be picky but the English term for the “second kind” phase transitions are “second order phase transition”.

And I don’t want you to panic but the transition from the liquid-like to gas-like supercritical CO2 is actually a higher-order phase transition

http://pubs.acs.org/cgi-bin/ab.....1803p.html

which might even be somewhat manifest in the video you included because the video is damn continuous and smooth, isn’t it?

Best
Lubos