Statistical measure of complexity and correlated behavior of Fermi systems

We apply the statistical measure of complexity, introduced by L'{o}pez-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.

💡 Research Summary

The paper investigates the applicability of the López‑Ruiz, Mancini and Calbet (LMC) statistical measure of complexity to uniform Fermi systems. The LMC complexity C is defined as the product of the information entropy H and the disequilibrium D, where H quantifies the spread of the momentum‑space probability density ρ(p) and D measures its deviation from a uniform distribution. By evaluating H and D for several interacting Fermi liquids—nuclear matter, the electron gas, and liquid helium‑4—the authors explore how C responds to the strength of many‑body correlations.

For nuclear matter the authors employ Brueckner‑G‑matrix theory together with a Jastrow correlation factor to obtain the dynamic structure factor S(k), which is Fourier‑transformed to yield ρ(p). In the electron gas, Random Phase Approximation (RPA) and a parametrized correlation energy ε_c are used to incorporate exchange‑correlation effects. For liquid helium‑4, quantum Monte‑Carlo data for S(k) and the pair‑distribution function g(r) are taken from experiment and simulation. In all three cases the calculated complexity rises non‑linearly with increasing correlation strength; a pronounced peak appears when the correlation energy constitutes roughly 20–40 % of the total binding energy, indicating that C can serve as a quantitative index of correlation.

The temperature dependence of C is examined for an ideal (uncorrelated) Fermi gas. Using the temperature‑dependent chemical potential μ(T) and the Fermi‑Dirac occupation f(p,T)=1/