The choice of denominator letters are not irrelevant in Leibniz notation. They are chosen in conjunction with parameterization in order to suppress arguments to

The choice of denominator letters are not irrelevant in Leibniz notation. They are chosen in conjunction with parameterization in order to suppress arguments to avoid being lengthy. Similar to how Einstein summation convention is used to suppress summation symbols. All notational conveniences lead to confusion in certain scenarios. Given a field W, you will want to talk about various derivatives of the field. However, you might not be interested in the derivative of the fields with respect to coordinate fields like `\partial W / \partial x^i`, you might be interested in derivatives of that field with respect to some other field like `\partial W / \partial \lambda_i`. Then you end up introducing all kinds of auxiliary notation for the functional representations of the field. You end up with `\tilde{W}(\lambda_i)` and `\bar{W}(I_i)` next to `W(x_i)`. Or just consider changes of variable, one generally doesn't distinguish the electric field `E` from cartesian, to axisymmetric, to spherical to whatever other coordinate system you dream up. Instead, the presence of the chosen coordinate symbols denotes the coordinate system in use and you don't need to distinguish the field from its functional representation. In order to understand `\partial_2 E` you would need to understand what coordinates I am working with while `\partial E / \partial y` is a bit more self explanatory in classical electrodynamics. Thermodynamics picks up confusion because of the constant changes in variable when the variables aren't coordinates.