I may be wrong, but I think the filters are not passive. There is in fact a chemical reaction going on, and energy (stored in the chemistry of the filters) is

I may be wrong, but I think the filters are not passive. There is in fact a chemical reaction going on, and energy (stored in the chemistry of the filters) is being consumed to capture the CO2. There are rocks - concrete does it too - which absorb CO2. This also is a chemical reaction, where the rocks and the concrete are giving up energy to capture the CO2.