A detailed comparison between collisionless and weakly collisional slab ion temperature gradient (ITG) driven turbulence is made by the Eulerian kinetic simulation of high accuracy [1]. It is confirmed that, in the limit of weak collisionality, the turbulent thermal diffusivity in the steady state of the collisional turbulence coincides with that in the quasisteady state of the collisionless turbulence [2] although, in the latter case, the entropy associated with the fine-scale structure of the distribution function in the velocity space grows indefinitely in time. Also, a spectral analysis of the velocity distribution function is done to investigate the entropy transfer from macro to microscales through phase-mixing processes. It is shown that the entropy spectrum obeys a power law in the range that is free from instability sources and collisional dissipation. An interesting analogy between the entropy spectrum in the ITG turbulence and the spectrum of a passive scalar quantity
in a turbulent fluid is discussed.

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