A novel method is proposed to construct collisionless fluid closures accounting for some kinetic properties. The idea consists in optimizing the agreement between the fluid and kinetic quasi-linear entropy production rates, so as to constrain the closure coefficients. This procedure is applied to the slab branch of the ion temperature gradient driven instability. Focusing on the kinetic regime characterized by slow waves, the closure proposed by Hammett and Perkins (Hammett and Perkins 1990 Phys. Rev. Lett. 64 3019) naturally emerges from the systematic identification of the kinetic and fluid entropy production rates. This closure is revealed to be extremely powerful well beyond the kinetic regime. Besides, it reconciles the fluid and kinetic linear stability diagrams in the two-dimensional space of the density and temperature gradient lengths. Such a method is systematic and generic. As such, it is applicable to other models and classes of instabilities.