Practical aspects -- how to change subfields between PhD and postdoc? For the context of the question, I'm interested in switching between different areas of a field -- e.g. I did my PhD in biological physics mainly involving simulations on a specific biological system, and I am now interested in pursuing more theoretical work (e.g. applied mathematics) still in biological physics but potentially on a different system.

So theoretically I know there should be no problem and my PhD should have prepared me for any new learning I need to do to catch up, but practically I'm wondering if there are 'better' ways of addressing some issues:


Background knowledge: I have some theoretical background, but not the familiarity of having done theoretical work daily in the past years. I would also have some catching up to do (probably several books to get through before I would be comfortable). When would be the best time to do this catching up? If I do it after beginning a postdoc, my postdoc work will be delayed during this (probably months) of catch-up time. Should I take time off between my PhD and postdoc? However then I have to explain an awkward unemployed period on my CV, and additionally not having an institution affiliation would take away my access to journals/libraries. 
Competitiveness as a candidate: If I were a PI, I would favour candidates who had demonstrated a capability in the field already. How can I demonstrate an ability to do theoretical work if it was not a large component of my PhD? One thought I had was to look within my own institution for a postdoc advisor since it might be easier to convince them, but I'm also aware that staying in the same institution for my postdoc could be a red flag later in my career. 


Also welcome tips on how to prepare for such an anticipated switch, if I still have a few years left of my PhD.
When would be the best time to do this catching up? If I do it after beginning a postdoc, my postdoc work will be delayed during this (probably months) of catch-up time.


A piece of post-doc advice that has worked for me is to have your fingers in several pies. Build up some new expertise while working on some low-hanging fruits from your existing background that will lead to immediate results.


  If I were a PI, I would favour candidates who had demonstrated a capability in the field already. How can I demonstrate an ability to do theoretical work if it was not a large component of my PhD?


The qualities that advisors are looking for may vary significantly. If they are looking specifically for a candidate with a strong theoretical background, there's only so much you can do. Others will prioritize broader research skills, like


a strong ability to finish projects (which you can show by building an appropriate track record; so be sure to have your pending papers out before you apply), and 
a strong ability to tell a good story (which you can show by being outstanding in your application materials and communication to them; basically, explain how you will help their team succeed based on your expertise).