  We analyze the waiting time distribution of time distances $\tau$ between two
nearest-neighbor flares. This analysis is based on the joint use of two
distinct techniques. The first is the direct evaluation of the distribution
function $\psi(\tau)$, or of the probability, $\Psi(tau)$, that no time
distance smaller than a given $\tau$ is found. We adopt the paradigm of the
inverse power law behavior, and we focus on the determination of the inverse
power index $\mu$, without ruling out different asymptotic properties that
might be revealed, at larger scales, with the help of richer statistics. The
second technique, called Diffusion Entropy (DE) method, rests on the evaluation
of the entropy of the diffusion process generated by the time series. The
details of the diffusion process depend on three different walking rules, which
determine the form and the time duration of the transition to the scaling
regime, as well as the scaling parameter $\delta$. With the first two rules the
information contained in the time series is transmitted, to a great extent, to
the transition, as well as to the scaling regime. The same information is
essentially conveyed, by using the third rules, into the scaling regime, which,
in fact, emerges very quickly after a fast transition process. We show that the
significant information hidden within the time series concerns memory induced
by the solar cycle, as well as the power index $\mu$. The scaling parameter
$\delta$ becomes a simple function of $\mu$, when memory is annihilated. Thus,
the three walking rules yield a unique and precise value of $\mu$ if the memory
is wisely taken under control, or cancelled by shuffling the data. All this
makes compelling the conclusion that $\mu = 2.138 \pm 0.01$.

Statistical Mechanics