Here's an article[1] trying to define the term a bit more rigorously. Here we discuss a sharp definition of the narrow concept of emergence in physics; we give

Here's an article[1] trying to define the term a bit more rigorously. Here we discuss a sharp definition of the narrow concept of emergence in physics; we give a mathematically precise meaning to the notion of ‘qualitative difference.’ We propose the following: An emergent behavior of a physical system is a qualitative property that can only occur in the limit that the number of microscopic constituents tends to infinity. Which is essentially the opposite of what you mention (vanishes when looking at the microscopic constituents). [1]: https://www.nature.com/articles/npjquantmats201624 https://www.nature.com/articles/npjquantmats201624