Statistically steady states of the ion temperature gradient driven turbulence with weak collisionality, where the collision frequency is much lower than characteristic ones of the turbulence, are investigated by means of a Eulerian kinetic simulation with high resolution. In the saturated state of the entropy variable, the ion heat transport balances with the collisional dissipation that is indispensable to realizing a steady-turbulence state of perturbed distribution function deltaf. The kinetic simulation definitely confirms the conventional hypothesis that, in a low-collisionality limit, the low-order velocity-space moments of deltaf as well as the ion heat transport flux agree with those in the quasisteady state of the collisionless turbulence with the constant entropy production. A spectral analysis of deltaf in the velocity-space clarifies the transfer and dissipation processes of the entropy variable associated with fluctuations, where the phase mixing, the E×B nonlinearity, and the finite collisionality are taken into account. A power-law scaling predicted by the theoretical analysis is also verified by the simulations in a subrange of the power spectrum which is free from the entropy production and the collisional dissipation.
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