Information & Complexity in the Universe

I am exploring quantiative ways to define, study and display how complexity grows in large-scale structures, and how the information flows across them while they grow. 


    ​In a recent work appeared in the Monthly Notices of the Royal Astronomical Society ( Vazza F., 2016 ), I have  investigated for the first time the application of Information Theory to the evolution of clusters of galaxies. Self-gravitating systems where hundreds of galaxies are bound together and very diluted plasma are heated up to temperatures of billions of degrees, clusters of galaxies are still forming nowadays and when gaseous matter falls into them under the pull of their ever-reaching gravitational potential, it gets shocked and turbulent, generating complex behaviors that can be modeled with advanced numerical simulations. While the past epochs of formation of galaxy clusters cannot be observed in Nature, with the help of supercomputers (currently using up to tens of millions of CPU hours per simulation) we can simulate the likely formation scenario of such objects, and dissect the emergence of complex pattern along their evolutionary path .
Using these datasets, we can dissect the self-organisation of the string of symbols (i.e. field values) generated by the simualtion while running. The information entropy associated with the flucutation of such variables, both in space & time, allows us to measure how difficult to predict ("complex") different components of such system are. 


Methods & Results

 The emergence of complex evolutionary patterns can be studied with a ​​statistical symbolic analysis of the datastream produced by a cosmological simulation. 
This 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  statistical complexity   and the  block entropy   turned out to be very powerful tools to quantify complexity in these simulations.

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. The evolution of the magnetic field is twice as complex, because it 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, because additional mechanism like cooling and feedback can now alter the time evolution of the energy components of the intracluster medium, and make their evolution more difficult to predict. (->)

Magnetic complexity [bits]            Thermal complexity [bits] 

"The Strange Similarity of Neuron and Galaxy Networks" popular article in

A popular article appeared in the 50th issue of the US online magazine "", "Emergence".
...feautring our semi-quantiative analysis of the similarities between the neuronal network and the cosmic web. 
See article online here .


F. Vazza (IRA/INAF, Bologna)
A. Feletti (NOCSAE Hospital, Azienda Ospedaliero-Universitaria di Modena, Italy)