We have used molecular dynamics (MD) simulation to investigate ionic self-diffusivity in NaAlSi2O6 melts and glasses at pressures of 3--58 GPa and temperatures of 2500--5000 K, to evaluate the effectiveness of a two-body potential in reproducing pressure and temperature dependence of tracer self-diffusivities. For each species, self-diffusivity increased with increasing temperature; with increasing pressure up to ~15 GPa, the self-diffusivity of O, Si, and Al increased, while mobility of Na decreased. An Arrhenian fit to self-diffusivity data collected from simulations at temperatures above the kinetic glass transition (up to 15 GPa) gives for activation energy (Ea) and activation volume (Va): Na: Ea(kJ/mol)=81¿14, Va(¿106 m3/mol)=3.5¿0.5, log D* (m2/s)=-6.8¿0.17; Al: Ea=306¿31, Va= -5.6¿1.1, log D* =-6.5¿0.35; Si: Ea=294¿23, Va= -6.1¿0.9, log D* =-6.9¿0.26;O: Ea=302¿23, Va= -5.9¿0.8, log D* =-6.6¿0.26. The MD-derived Ea,O and Va,O agree with laboratory results of 275¿10 kJ/mol and -6.2¿0.6 cm3/mol for Ea,O and Va,O respectively [Shimizu and Kushiro, 1984> measured in experiments at 1673 to 1923 K and 0.5 to 2 GPa. Agreement with the pre-exponential factor (D*) is poorer, with MD result of ~10-6.6 for O and laboratory value ~10-4.7. From ~15 GPa--25 GPa, Va is ~0 m3/mol for O, Si, and Al; these species have a positive Va for pressures above 25 GPa (Va,O is ~+1 cm3/mol). For pressures ~15 GPa the majority of the network cations are in 5- or 6-fold coordination, and more than 20% of the O is in 3-fold coordination. With increasing pressure, 4-fold Si and Al decrease monotonically, while 6-fold Si and Al increase monotonically. Pentahedral Si and Al maximize at nearly the same pressure as O self-diffusivity.¿ 1997 American Geophysical Union