Negentropy as Diagnostic of Cosmic Density Fields and Dynamical Dark Energy Models

We employ negentropy ($J$), defined as the difference between the information content of a non-Gaussian probability distribution and a Gaussian with identical variance, as an information-theoretic probe of non-Gaussianity in the cosmic density field. We quantify its sensitivity to dynamical dark energy by studying the evolution of $J(a)$ and its derivatives $\Gamma_1(a)$ and $\Gamma_2(a)$ across three parameterisation schemes: CPL, JBP, and BA. We determine the characteristic redshift $z_{NG}$, marking the epoch of maximal non-Gaussian structure formation, and the turnaround redshift $z_{TA}$, when information production transitions due to dark-energy domination, finding $z_{NG}\sim0.81$ and $z_{TA}\sim0.18$ for $\Lambda$CDM. Our diagnostics clearly discriminate between thawing and freezing quintessence models and phantom dark energy at low redshifts. Thawing models show small departures from $\Lambda$CDM, freezing models display higher $z_{TA}$, while phantom models exhibit lower $z_{TA}$, reflecting late-time evolution. We provide a practical prescription for measuring negentropy from discrete galaxy distributions, establishing a framework that can be applied to simulations and observations. This information-theoretic approach offers a robust and complementary tool for probing dark energy dynamics, enabling sensitive discrimination between evolving and cosmological-constant scenarios.