Intensive Variables: Equal Value for Equilibrium?

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Intensive variables must have the same value at all points in a system at equilibrium, as they are scale invariant. The discussion emphasizes the importance of reasoning and encourages participants to share their thought processes for constructive feedback. Electric and magnetic fields are identified as intensive variables, prompting further exploration of their behavior in thermal equilibrium. Understanding these principles is crucial for analyzing systems in equilibrium. The conversation aims to deepen comprehension of intensive variables in the context of electromagnetic fields.
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Is it a necessary condition for intensive variables to have the same value for all points in a system that is in equilibrium?
 
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We can't just give you the answer, since then nobody would learn anything. But if you describe your reasoning, you'll likely get helpful comments.
 
My reasoning is that they are said to be scale invariant. I read that electric and magnetic fields can be taken to be intensive, so I'm just trying to narrow down what is considered in an electromagnetic field in thermal equilibrium.
 
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