On the complexity and the information content of cosmic structures

Abstract

The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to measure the information content of cosmic structure and to quantify the complexity that emerges from it, based on Information Theory. The emergence of complex evolutionary patterns is studied with a statistical symbolic analysis of the datastream produced by state-of-the-art cosmological simulations of forming galaxy clusters. This powerful approach allows us to measure how many bits of information are necessary to predict the evolution of energy fields in a statistical way, and it offers a simple way to quantify when, where and how the cosmic gas behaves in complex ways. The most complex behaviors are found in the peripheral regions of galaxy clusters, where supersonic flows drive shocks and large energy fluctuations over a few tens of million years. Describing the evolution of magnetic energy requires at least a twice as large amount of bits than for the other energy fields. When radiative cooling and feedback from galaxy formation are considered, the cosmic gas is overall found to double its degree of complexity. In the future, Cosmic Information Theory can significantly increase our understanding of the emergence of cosmic structure as it represents an innovative framework to design and analyze complex simulations of the Universe in a simple, yet powerful way.

How complex is the cosmic web?

“…The inclusion of AGN activity thus creates an additional mechanism for the sudden variation of magnetic and thermal energy values in the simulation (as well of kinetic energy via outflows, not shown here). This, in turn, adds complexity to the evolution of baryons, at least in the close proximity of AGN events, up to Cµ ∼ 10 2 bits/cell (see last column of Fig.15), as already noticed in earlier work (Vazza 2017).…”

“…Therefore, while in Vazza (2017) I degraded the resolution of the simulation in order to measure complexity on the best scale, for this work I directly generated simulations resolving the optimal scales to study complexity, i.e. ∆x = 100 kpc/h ∼ 142kpc for all simulations.…”

“…Following Vazza (2017), I monitored the evolution of cosmic matter in the simulated universe by focusing on the evolution of the energy fields associated to normal baryons: the gas kinetic energy (E k = (1/2)ρv 2 dV within each cell), the gas thermal energy (Et = (3/2)k b ρT /(µmp)dV ) and the magnetic field en-…”

“…where the volume integral is over the cell size 3 . As already noted in Vazza (2017) there is no unique way of partitioning the internal energy of a cosmological simulation. For this reason, the arbitrary choice of how to partition the system into a set of discrete states is the result of a compromise between the need of keeping the computing resources under control (as the computation of the statistical complexity scales as ∝ N 2 bin (where N bin is the number of energy bins) and the capability of resolving all relevant energy transitions between close timesteps.…”

“…It shall be noticed that the computing problem here is non trivial, as the computation of statistical complexity for NE = 3 energy fields requires to generate an N bin × N bin matrix of transition probabilities across 2 subsequent snapshots for the entire sequence of Nstep snapshots, for NE × n 3 dataset at every iteration (where n = 400 cells in this case). Compared to Vazza (2017), in which routines in IDL were developed to compute statistical complexity and block entropy of cosmological simulations, in this work I implemented the above algorithm in Julia language (https://julialang.org), for computing speed reasons.…”