among them, the non-equilibrium properties, given by the spectrum of $\hat W$.

Next, we shall describe the methodology for the case of a $16x16\times 16$ lattice size for an orbit of $E=-292$ and a period $T= 43115258$. The probability transition matrix $\hat W$ is constructed following the steps of the previous section \[masterEqn\]. But first, we shall verify that the master equation does not strongly depend on the length of the time series for the magnetization. It is important to underline that we think that this is a crucial step, because it allows us to compare explicitly the dependence of the results on the partial length of the cycles. Something not possible in larger systems, because in these cases we shall never be able to build the complete period for the time series.

To test that, we shall use again the finest partition. In this case the transition matrix has dimension $257 \times 257$ (so we shall not provide them explicitly) and we shall characterize it by the equilibrium distribution, and the full set on eigenvalues of $\hat W$. Fig. \[Method\] (a) and (b) plot the equilibrium distribution ${\bm f}_{eq} $ and the set of 257 eigenvalues for the same 