Can someone provide an overview of the thermodynamics of DAC?

Direct Air Capture (DAC) and related methods for CO2 capture and sequestration are often offered as an eventual solution to excess atmospheric CO2.

It seems well understood that current technology in this space is not sufficient and preliminary in terms of success and results, but it also seems to be the case that plenty of serious attention and resources are being directed into this general approach.

I'm wondering if someone can provide us with an overview / breakdown of the thermodynamics involved in this type of methodology.

There's surely a hard minimum on the amount of energy required to remove CO2 from the atmosphere (moving the air, breaking the bonds of the molecules, pumping or transporting the post-reaction products, etc). There's also the issue of the carbon emissions required to produce these facilities to begin with (even if we assume all energy inputs are derived from renewable sources).