I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times Q)=S_q(P)+S_q(Q)+(1-q)S_q(P)S_q(Q)$. My question is what is meant by nonextensive statistical physics? What is its connection with Tsallis entropy maximisation?
Normally entropy is seen as an extensive thermodynamic coordinate, i.e. proportional to the mass of particles: Volume increases by considering a larger amount of gas in the "same state", while pressure will stay the same. So for simple systems entropy of a system that is a combination of 2 systems will be sum of individual entropies. Here it is less. This means that not the whole direct product of states of A and states of B is accessible to the combined system. Consider a state space of 3x3 pixels for a particle A alone: 9 states. consider B to be an identical system: also 9 states. Now assume you can put A and B in the same 3x3 pixel space and allow them to also sit in the same pixel: 9x9=81 states, however suppose that they interact such that they can not sit in the same pixel:9x9 - 9=72 states so in this second example entropy is not additive for combination of systems. while it is in the first...