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The sentence in which I use it similar to the following:

From this, it is possible to define a diffusion-time-dependent dimension.

I am not sure if the double hyphenation is correct or not, but I cannot rephrase the sentence with other words, so, please, don't suggest particular changes.

Furthermore, "diffusion time" is often found in literature without a hyphen, so maybe "diffusion time-dependent" is the correct choice, but it seems a bit wrong to me...

Could you explain what are the general rules for cases like this?

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  • Diffusion time-dependent is an incorrect choice as it wrongly indicates that the cohesion between 'time' and 'dependent' is greater than that between 'diffusion' and 'time' (at least a strong collocation [and perhaps a compound] as you say). A tricky one. Some might suggest hyphen plus dash, but I think that's rare and rarefied. I'd use the double dash. But it's awkward as diffusion time isn't itself hyphenated. // I don't think this precise compound premodifier (or is it?) problem has been addressed before.
    – Edwin Ashworth
    Oct 1, 2020 at 10:50

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Given that time-dependent is hyphenated when used to say that something depends on time, and diffusion time is a particular kind of time, I think that the two hyphens is a good idea, since you want to make sure that it is "diffusion time" that you are depending on, not just time. But I am not an expert.

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For the general rules on compound adjectives, I would refer to your favorite style guide. (Mine is Chicago Manual of Style.)

You might take a look at this question and this answer (in regards to CMoS, en-dashes, and compound adjectives).

For your specific question, you need to ask yourself: Does this adjective stand on its own, or does it need the other(s) in order to make sense?

For example, these don't make sense:

? a diffusion-time dependent dimension (there is no such thing as a dependent dimension)

? a diffusion time dependent dimension (there is no such thing as a dependent dimension or a diffusion dimension)

However, these might make sense

a diffusion time-dependent dimension (very often the x-axis is the time-dependent dimension)

a diffusion-time-dependent dimension (if there is a contrast between the diffusion-time-dependent dimension and the suffusion-time-dependent dimension; this seems to be what the author is proposing.)

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