The maximum entropy principle and the stochastic aspects of deterministic chaos

We obtain the evolution equation for the coarse-grained distribution associated with the Perron–Frobenius equation, analyzing the conditions under which it reduces to a Chapman–Kolmogorov equation. This is achieved using two methods, one of them due to G. Nicolis and C. Nicolis in terms of two assumptions, and another one using information theory concepts such as the maximum entropy principle and the principle of operational compatibility.