Say we built two large scale portals and sent one to Venus and one to Mars much like in this question but with portals large enough that mass flow rates are not an issue seeing as nobody wants to wait around for 108 billion years for some more habitable planets.
The idea is to dump some of Venus' atmosphere on Mars to get it up to a reasonable temperature, thus leaving us with two semi-terraformed planets rather than just one. (the rest of Venus' excess atmosphere gets dumped out in space and so isn't part of our energy problem)
Now in one of the answers, Demi pointed out that naturally, gas would flow towards Venus despite a 15'000:1 difference in ground-level atmospheric pressure as Venus sits much deeper in the Sun's gravity well. Hence our problem, we need to relocate some of Venus' atmosphere to Mars but just how big of a power station are we going to need...
What I'd like to know is: assuming that we built a whole fleet of air-compressors to force Venus' atmosphere to Mars through our portal (ideally before the end of the millennium), just how much energy would we realistically need to achieve this? (assuming that the portals only represent a small fraction of the total energy expenditure)
Edit: these portals do conserve energy and momentum, if they didn't then all we'd need to worry about is the atmospheric pressure difference. But, when we start adding gravity wells (gravitational potential energy) and orbital velocity (kinetic energy) then the end result becomes... too much for my brain to get a grip on. Something bad presumably if the current answers are anything to go by.