For example, is there a difference in result if I adjust the exposure slider then make a change in the tone curve vs if I do the same operations in the reverse order? My suspicion based on instinct and casual observation is that some operations do commute, but most do not. Can anyone shed more light on this? Are there particular pairs of operations which produce important or dramatic differences depending on order?
According to what I've read, the Develop Pipeline is fixed and specific. The order in which the adjustments are applied is irrelevant. It is the final position of the sliders is the determining factor.
Agreed, actually when working in the develop module Lightroom works with the original file and re-renders the file with every adjustment made and as Rikk says the adjustments are applied in a specific order. If you have made several changes to a particular setting e.g saturation, clarity, exposure it will render the net effect of each.
Are you saying that regardless of which order in which I actually apply the editing adjustments, LR rerenders the editing changes applying adjustments in its predetermined order. So, in my original post example if LR wants to apply Exposure adjustments before Tone Curve adjustments, it will do so even if I change the tone curve before I move the Exposure slider. If this is the case, is the predetermined order that LR uses essentially the top down order of controls on the Basic panel or something else?
The predetermined order is not published. We can make guesses at the actual order but they are only guesses.
Whether you apply exposure as your first editing step or your last makes no difference. The rendering pipeline will apply it within a prescribed order.
As far as I am aware LR has not published the specific process order that it uses to render the final image. So the order you make the adjustments you wish to apply will not affect the final rendered image.