The upper atmosphere has an electrodynamic dimension (related to the increasing presence of plasma with elevation) that renders it susceptible to the influence of the flow of charged particles from the sun.
This is a muddled and misunderstood and vague and somewhat wrong description of things. I have pointed that out to Erl dozens of times, but he refuses to learn.UV from the Sun [not charged particles] basically creates the ionosphere, and heats the upper atmosphere causing it to expand. In addition, there are currents flowing into the polar ionosphere from the tail of the Earth’s magnetosphere [not from the Sun]. These currents heats the upper atmosphere too.
This may be responsible for the change in surface pressure at the poles in relation to that at the equator
The density of the atmosphere decreases by a factor of 1000 for each 50 km you ascend, so up in the ionosphere and thermosphere the density is down by a factor of a million [at 100 km] to a trillion [at 200 km], and expansion of contraction of whatever of that small amount of air has no measurable effect on surface pressure.
Out of curiosity, to what do you ascribe the LIA?
Nobody knows. One could guess internally driven oscillations e.g. involving the oceans.