[Paper Review] Statistical measure of complexity in compact stars with global charge neutrality

Rodrigo Alvares de Souza, Márcio G. B. de Avellar+1 more|arXiv (Cornell University)|Aug 15, 2013

Statistical Mechanics and Entropy3 citations

TL;DR

This paper introduces an information-theoretic approach to assess the complexity of compact stars under global charge neutrality, using the statistical complexity measure $ C = e^H D $, where $ H $ is Shannon entropy and $ D $ is disequilibrium. It finds that global charge neutrality and strong interactions reduce disequilibrium, pushing neutron stars toward a more disordered, ideal-gas-like state, with complexity values decreasing under global neutrality compared to local neutrality.

ABSTRACT

Recently, it has been suggested that a critical electrical field arises during the gravitational collapse of massive stars leading to a vacuum polarization. This, in turn, leads to the necessity of a reexamination of the gravito-electrodynamical properties of compact stars of the class of neutron stars. Rotondo, Rueda, Ruffini and Xue claim to have proved the impossibility of local charge neutrality and then solved the coupled system of the general relativistic Thomas-Fermi-Einstein-Maxwell equations for the structure of neutron stars. Within the same approach of Avellar and Horvath (2012) we have calculated how the global neutrality hypothesis affects the order/disorder of these systems for a simple equation of state. We show the relative preference of local vs. global conservation in terms of the obtained information content of the systems under consideration.

Motivation & Objective

• To investigate the impact of global charge neutrality on the statistical complexity of compact stars using information-theoretic measures.
• To extend previous studies based on local charge neutrality by incorporating global charge neutrality and strong interactions in neutron star structure models.
• To validate the use of density profiles as probability distributions for calculating information content, avoiding negative entropy values.
• To explore whether neutron stars become more or less complex with increasing mass under global charge neutrality.
• To reconcile discrepancies in complexity trends observed in prior studies by re-examining the behavior of $ e^H $ and $ D $ in self-gravitating systems.

Proposed method

• Uses the statistical complexity measure $ C = e^H D $, where $ H $ is Shannon entropy and $ D $ is the disequilibrium from deviation from uniform probability distribution.
• Applies the complexity measure to neutron star sequences derived from exact solutions of the Tolman-Oppenheimer-Volkoff (TOV) equations with anisotropic pressure and MIT bag model equation of state.
• Implements a modified density profile that satisfies probability constraints: $ p(x) \in [0,1] $ and $ \int p(x)dx = 1 $, to avoid negative information entropy.
• Solves the coupled Einstein-Maxwell-Thomas-Fermi equations to model neutron stars under both local and global charge neutrality conditions.
• Compares complexity, entropy, and disequilibrium between global and local charge neutrality cases using numerical results from reference [6].
• Validates the physical consistency of the probability-like density profile using exact solutions of the Einstein equations.

Experimental results

Research questions

• RQ1 How does global charge neutrality affect the statistical complexity of neutron stars compared to local charge neutrality?
• RQ2 What is the behavior of the information entropy $ H $, disequilibrium $ D $, and complexity $ C $ in neutron stars under global charge neutrality?
• RQ3 Does the inclusion of strong interactions alter the complexity profile of neutron stars in the context of global charge neutrality?
• RQ4 Why do complexity trends in this study differ from prior claims that neutron stars do not grow more complex with increasing mass?
• RQ5 Can the neutron star density profile be consistently treated as a probability distribution for information-theoretic analysis?

Key findings

• For $ \rho_{\text{crust}} = 10^{10} \, \text{g/cm}^3 $, global charge neutrality yields a lower complexity ($ C = 16.947 $) than local neutrality ($ C = 15.583 $), despite higher mass and radius in the global case.
• At $ \rho_{\text{crust}} = 4.3 \times 10^{11} \, \text{g/cm}^3 $, global charge neutrality results in $ C = 14.474 $, slightly higher than local neutrality ($ C = 13.858 $), indicating a non-monotonic trend.
• The disequilibrium $ D $ is reduced under global charge neutrality: $ D = 30.441 $ (global) vs. $ D = 36.611 $ (local) at $ \rho_{\text{crust}} = 10^{10} \, \text{g/cm}^3 $, indicating a shift toward more uniform state distribution.
• The information entropy $ H $ is less negative under global charge neutrality ($ H = -0.586 $) than under local neutrality ($ H = -0.840 $), suggesting reduced uncertainty or increased order.
• The results suggest that global charge neutrality and strong interactions tend to reduce disequilibrium, pushing the system toward a more disordered, ideal-gas-like state in the complexity-intuition plot.
• Discrepancies with prior claims that neutron stars do not grow more complex with mass arise from the relative rates of change of $ e^H $ and $ D $, particularly due to the sign of $ H $, requiring further investigation.