  We introduce a second-order gyro-averaged extension to a guiding-center
transport model for test particles subject to an $\mathbf{E}\times\mathbf{B}$
drift in a tokamak. Using this approximation, we numerically investigate the
influence of finite Larmor radius effects on the chaotic transport and the
formation of transport barriers. For non-monotonic plasma profiles, we show
that the twist condition of the system is violated along a curve, usually
called shearless transport barrier, which, under non-equilibrium conditions,
exhibits significant resilience to destruction, thereby inhibiting chaotic
transport. We analyze bifurcation diagrams of the shearless barriers and escape
rates to explore the impact of the Larmor radius on controlling chaotic
transport while varying the amplitude of electrostatic perturbations. Our
findings show that increasing the Larmor radius enhances the robustness of
transport barriers, as a larger electrostatic perturbation amplitude is
required to disrupt them. Additionally, even in the absence of transport
barriers, we observe a decrease in chaotic transport with an increase in the
Larmor radius.
