How should I break-up with a second author?
Has he offered a timeline when he might be able to do his part? Have you had any communication regarding this? If not, you should reach out in advance and offer your timeline, giving him a reasonable timeframe to complete his work.

If you've had such communication before, and he hasn't been able to stick to agreed upon dates, I think you should talk to your advisor and explain the situation. Then, you could write a very polite email to him, including your advisor and any other stakeholders, explaining that you need to submit this work soon. At this point you could ask him if he still has time and would be able to complete his section, say within one month. Mention that you understand he is busy and has multiple priorities to juggle, and that if there isn't time, you'd just like to concentrate on your part and submit it. If, at a later stage, you both have time, you'll be willing to work together if he'd like to submit the theoretical section separately, with him as the first author.

I think this will sound pretty reasonable and you'll be able to publish without antagonizing or destroying working relationships with anyone.