The difference between order parameter and state parameter?

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State parameters like pressure, temperature, and volume are essential for fully describing a thermodynamic system, while the order parameter characterizes specific properties of the system. In Landau theory, the order parameter is treated as an external parameter rather than an independent variable because the free energy is expanded in terms of it, indicating its dependence on other thermodynamic variables. The discussion highlights that while the order parameter is often analyzed in relation to temperature, it can also be influenced by other thermodynamic variables. This leads to the conclusion that the order parameter can indeed be treated as an independent thermodynamic variable through appropriate transformations. Overall, the relationship between order parameters and state parameters is complex, yet they are interconnected in thermodynamic descriptions.
Diracmai
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At first, we need some state parameters(like P/T/V) to fully describe a system. And the order parameter is also a parameter which could describe the property of the system.
However, in the Laudau theory, why it said that order parameter is an external parameter(not a independent variable)? Is there any different between order parameter and state parameters(like P/T/V etc.)?
 
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I would say no, as in Landau theory we expand the free energy into a power series in the order parameter. Hence it must be a thermodynamic variable.
 
DrDu said:
I would say no, as in Landau theory we expand the free energy into a power series in the order parameter. Hence it must be a thermodynamic variable.
Ok! Actually, I also take the some viewpoint as you. In addition, I have another question.Generally, when we use Laudau phase transition theory, we always choose T and order parameter as free energy's variables. In this condition, it that means we hold other thermodynamic variable as constant and only discuss the relation between order parameter and temperature. In fact, the order parameter can also be the function of other thermodynamic variables.
 
Diracmai said:
In fact, the order parameter can also be the function of other thermodynamic variables.
Isn't this trivial? E.g. you can describe a gas in terms of V and T or in terms of p and T, the transformation being P(T,V). So you can always introduce the order parameter as an independent thermodynamic variable.
 
A relative asked me about the following article: Experimental observation of a time rondeau crystal https://www.nature.com/articles/s41567-025-03028-y I pointed my relative to following article: Scientists Discovered a Time Crystal That Reveals a New Way to Order Time https://www.yahoo.com/news/articles/scientists-discovered-time-crystal-reveals-180055389.html This area is outside of my regular experience. I'm interested in radiation effects in polycrystalline material, i.e., grain...

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