Meaning of a formula about transient frequency bins
without reading the paper,

Eqn 4 has the form of a central difference form of the second derivative. It is a numerical second derivative compared to a threshold. It differs from the standard form in that it centers on $n-1$. 

https://en.m.wikipedia.org/wiki/Finite_difference

Whatever $\phi$ is, it is the positive change compared to a threshold.