From the definition of the Shannon’s information (see Eq. (11)),
it follows that the maximum entropy is attained by considering
an equiprobability situation. Thus, the simplest assumption
for the maximum entropy would be that S max ∝ ln(N∗), where
pk = 1/N∗. This situation corresponds to the case of an isolated
(microcanonical) system based on the assumption, as a postulate,
of a uniform probability for all the microstates corresponding
to the same macrostate (Ben-Naim 2008). Although this is a
reasonable hypothesis, its applicability to the solar cycle dynamics
is questionable. In the case of solar cycle dynamics, we deal
with a nearly stationary nonequilibrium state, where the assumption
of equiprobability for the occupation number (state amplitude)
could lead to an overestimation of the reference maximum
entropy. This point is also corroborated by the assumption of
Shiner et al. (1999) of assuming S eq to be the reference maximum
entropy. In other words, we have to find a way of defining
a reasonable reference stationary distribution ˆpk to be able to
evaluate the reference maximum entropy.