A set of flux tube gyrokinetic equations that includes the effect of the
spatial variation of the density, temperature and rotation gradients on the
turbulence is derived. This new set of equations uses periodic boundary
conditions. In the limit $l_\bot/L \ll 1$, where $l_\bot$ is the characteristic
perpendicular length of turbulent structures and $L$ is the characteristic size
of the device, this new set of flux tube gyrokinetic equations is shown to be
equivalent to the traditional global $\delta f$ gyrokinetic equations to an
order higher in $l_\bot/L$ than the usual flux tube formulations.