Statistical measure of complexity and correlated behavior of Fermi systems

We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini, and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas, and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.

Figure 1

$S_{\text{cor}}$, $D_{\text{cor}}$, and $C$ of nuclear matter versus the correlation parameter $k_{\text{dir}}$. The lines correspond to the expressions (27, 28, 29), with the parameters derived by the least-squares fit method.

Figure 2

(a) The momentum distribution for correlated nuclear matter versus $k/k_F$ for various values of the correlation parameter $k_{\text{dir}}$. (b) The momentum distribution of an ideal electron gas versus $k/k_F$ for various values of the ratio $T/T_F$.

Figure 3

(a) $S_{\text{cor}}$, (b) $D_{\text{cor}}$, and (c) $C$ for nuclear matter, electron gas, and liquid helium versus the discontinuity parameter $\left(1-Z_F\right)$. In the case of liquid helium, the values of $S_{\text{cor}}$ are divided by 10 and the values of $C$ by 100.

Figure 4

$S_{\text{cor}}$, $D_{\text{cor}}$, and $C$ of electron gas the correlation parameter $r_s$. The lines correspond to the expressions (31, 32, 33), with the parameters derived by the least-squares fit method.

Figure 5

$S_{\text{cor}}$, $D_{\text{cor}}$, and $C$ of liquid helium versus the correlation parameter ${\rho }_0$. The values of $S_{\text{cor}}$ are divided by 10 and the values of $C$ by 100. The lines correspond to the expressions (39, 40, 41), with the parameters derived by the least-squares fit method.

Figure 6

$S_{\text{thermal}}$, $D_{\text{thermal}}$, and $C$ of an ideal electron gas versus the ratio $T/T_F$.

Figure 7

(a) The complexity $C$ and the specific heat $C_V$ (in units $k_{B}N$) of an ideal electron gas versus the ratio $T/T_F$. (b) The specific heat $C_V$ versus complexity $C$.