By looking at the eigenvalue λk spe

By looking at the eigenvalue λk spectrum (see Fig. 2), we can
immediately realize that it is possible to define a reference ˆpk
distribution by again using our parallelism with quantomechanics.
By assuming that λk is equivalent to the occupation number
in the state | k of energy Ek ∝ k, it is indeed possible to introduce
an effective temperature Teff and a reference nearly exponential
distribution ˆpk for the reference stationary state. Figure 17
shows k ∝ Ek versus the natural logarithm of the occupation
number nk ≡ λk. A linear region can be found in the interval
range k ∈ [3, 18], from which an effective temperature Teff (data
not shown) can be estimated to be