"Temperature is loosely interpreted as the average kinetic energy of the system's particles. The existence of negative temperature, let alone negative temperature representing "hotter" systems than positive temperature, would seem paradoxical in this interpretation. The paradox is resolved by considering the more rigorous definition of thermodynamic temperature as the tradeoff between internal energy and entropy contained in the system, with "coldness", the reciprocal of temperature, being the more fundamental quantity. Systems with a positive temperature will increase in entropy as one adds energy to the system, while systems with a negative temperature will decrease in entropy as one adds energy to the system."
Not unlike the silly algebra tricks that “prove 0==1” and other such, which some of us played with at school. We had a good maths teacher who joined in, reasoned & unreasoned a few of them, and pointed us to off-curriculum things we might want to read. A nice lesson on the joy of thinking and applying critical thinking.
It's quite possible to have the apparent rate of separation of two particles, from the standpoint of third frame of reference, be superluminal. It happens in astronomical observations. See http://spiff.rit.edu/classes/phys200/lectures/superlum/super... for a nice example and explanation.
But you are quite right that from the frame of reference of either of the two particles sent traveling at .75c in opposite directions, the other particle is receding at subluminal velocity, not FTL.
