The imaginary planet of Daisyworld is the simplest model used to illustrate the implications of the Gaia hypothesis. The dynamics of daisies and their radiative interaction with the environment are described by fundamental equations of population ecology theory and physics. The parameterization of the turbulent energy flux between areas of different biological cover is similar to the diffusive-type approximation used in simple climate models. Here I show that the small variation of the planetary diffusivity adopted in the classical version of Daisyworld limits the range of values for the solar insolation for which biota may grow in the planet. Recent studies suggest that heat transport in a turbulent medium is constrained to maximize its efficiency. This condition is almost equivalent to maximizing the rate of entropy production due to non-radiative sources. Here, I apply the maximum entropy principle (MEP) to Daisyworld. I conclude that the MEP sets the maximum range of values for the solar insolation with a non-zero amount of daisies. Outside this range, daisies cannot grow in the planet for any physically realistic climate distribution. Inside this range, I assume a distribution of daisies in agreement with the MEP. The results substantially enlarge the range of climate stability, due to the biota, in comparison to the classical version of Daisyworld. A very stable temperature is found when two different species grow in the planet.