Tsallis Entropy and the Vlasov-Poisson Equations

We revisit Tsallis Maximum Entropy Solutions to the Vlasov-Poisson Equation describing gravita-tional N-body systems. We review their main characteristics and discuss their relationship with other applications of Tsallis statistics to systems with long range interactions. In the following con-siderations we shall be dealing with a D-dimensional space so as to be in a position to investigate possible dimensional dependences of Tsallis ' parameter q. The particular and important case of the Schuster solution is studied in detail, and the pertinent Tsallis parameter q is given as a function of the space dimension. In the special case of three dimensional space we recover the value q = 7=9, that has already appeared in many applications of Tsallis ' formalism involving long range forces.