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An entropy balance equation that maintains the dynamics in the radial direction is derived to study the role of zonal flows in turbulent transport. The equation describes the dynamics not only of the entropy density production related to zonal flow and local heat flux, but also of entropy density convection. We investigated these spatio-temporal dynamics of entropy in ion temperature gradient driven turbulence based on a global gyrokinetic Vlasov simulations in a slab geometry. The contribution of zonal flow to entropy production is observed to be small in the strong instability case, whereas the zonal flow energy is sufficiently large. We also found that the entropy density with n = 2 in the Hermite polynomial expansion in velocity space plays an important role in convecting the entropy density, causing turbulent spreading.

Gyrokinetic Study of the Local Entropy Dynamics in Turbulent Plasmas with Zonal Flow