A dynamical thermostatting approach to nonextensive canonical ensembles

We treat Tsallis generalized nonextensive thermostatistics through the method developed by Kusnezov, Bulgac, and Baller (1990) to simulate the canonical ensemble. Given a Hamiltonian system with a 2N-dimensional phase space, the introduction of two additional dynamical variables allows us to mimic the coupling of the original system to a thermal bath, yielding ergodic behavior. In this way, ensemble averages within the generalized nonextensive canonical ensemble can be obtained as temporal mean values evaluated on a trajectory of the extended dynamical system. We illustrate these ideas with some 1D and 2D examples. (C) 1997 Academic Press.