Extended phase-space dynamics for the generalized nonextensive thermostatistics

We apply a variant of the Nose thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a deterministic connection between the generalized nonextensive entropy and power-law behavior. For the case of a simple one-dimensional harmonic oscillator, we confirm by numerical simulation of the dynamics that the distribution of energy H follows precisely the canonical q statistics for different values of the parameter q. The approach is further tested for classical many-particle systems by means of molecular dynamics simulations. The results indicate that the intrinsic nonlinear features of the nonextensive formalism are capable of generating energy fluctuations that obey anomalous probability laws. For q<1 a broad distribution of energy is observed, while for q>1 the resulting distribution is confined to a compact support.