Undergrad Questions about deriving generic equations/laws from specific equations/laws

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The discussion focuses on the derivation of generic physical laws from specific equations, highlighting examples such as the relationship between electromagnetism and Ampere's law in the context of Maxwell's equations. Participants explore well-known generic laws, suggesting that general relativity and thermodynamics are foundational, as they govern all physical processes. In contrast, highly specific laws, like Newton's law of viscosity, are noted for their conditional nature, often applicable to particular scenarios or materials. The conversation emphasizes the importance of understanding how broader principles emerge from more specific laws in physics. Overall, the interplay between generic and specific laws is crucial in the study of physical phenomena.
Hallucinogen
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I'd like to ask what the most well-known case is of a formula for a physical law being derived from another (or set of others)?
For example, is there a law for electromagnetism that describes a law of electricity and a law of magnetism, which was derived from combining the two? Or any similar derivation? Does Ampere's law have this kind of relationship with Maxwell's equations?

Another related question is, what are the most well-known "generic" laws of physics which apply everywhere, and which are the most well-known highly specific laws of physics? I'd guess the most generic laws are those of general relativity and thermodynamics, since no physical process is allowed to conflict with them? And I'd guess that laws in materials science are highly specific, as they have multiple conditionalities, for example Newton's law of viscosity. Or laws about forces being applied to specific shapes?

Many thanks
 

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