Entropy network

Entropy networks have been investigated in many research areas,[1][2] on the assumption that entropy can be measured in a network. The embodiment of the network is often physical or informational. An entropy network is composed of entropy containers which are often called nodes, elements, features, or regions and entropy transfer occurs between containers. The transfer of entropy in networks was characterized by Schreiber[3] in his transfer entropy.

## Contents

* 1 Physical basis
* 2 Structures and motifs
* 3 Domains of study
* 4 References

## Physical basis

A discrete physical basis for entropy networks can be found in the observation, and discussions of discrete observations appear briefly in the work of Prokopenko, Lizier & Price.[4] More complete discussions of observations were offered by Leo Szilárd[5] and Léon Brillouin.[6]

## Structures and motifs

Network motifs have been proposed[7] to be scale independent. Networks have been classified by total entropy.[8] The entropy content of graphs has been considered throughout fields of math and computer science. Design of entropy networks and in depth investigation has been publicized by Wissner-Gross and Freer[9] who have proposed a time entropy relation (where entropy is maximized of a lifespan) through which predictions of the emergence of complexity can be shown.

## Domains of study

The role of entropy networks in formation of structures is critical in engineering and its physical implications determine chirality,[10] organize biological molecules,[11] and quantify the topologies of condensed matter (mass) networks.[12]

## References

1. ↑ Hu, Zhenjun; Snitkin, Evan S.; DeLisi, Charles (2008). "VisANT: an integrative framework for networks in systems biology". Briefings in Bioinformatics 9 (4): 317–325. doi:10.1093/bib/bbn020. PMID 18463131.
2. ↑ Deeds, Eric J.; Ashenberg, Orr; Shakhnovich, Eugene I. (2006). "A Simple Physical Model for Scaling in Protein–Protein Interaction Networks". PNAS 103 (2): 311–316. doi:10.1073/pnas.0509715102. PMID 16384916.
3. ↑ Schreiber, Thomas (2000). "Measuring Information Transfer". Physical Review Letters 85 (2): 461–464. doi:10.1103/PhysRevLett.85.461. PMID 10991308. Bibcode: 2000PhRvL..85..461S.
4. ↑ Prokopenko, Mikhail; Lizier, Joseph T. (2015). "Transfer Entropy and Transient Limits of Computation". Scientific Reports 4: 5394. doi:10.1038/srep05394. PMID 24953547.
5. ↑ Szilárd, Leo (1929). "Ü ber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen". Zeitschrift für Physik 53 (11–12): 840–856. doi:10.1007/BF01341281. Bibcode: 1929ZPhy...53..840S.
6. ↑ Brillouin, Léon (1953). "The Negentropy Principal of Information". Journal of Applied Physics 24 (9): 1152–1163. doi:10.1063/1.1721463. Bibcode: 1953JAP....24.1152B.
7. ↑ Angulo, Marco Tulio; Liu, Yang-Yu; Slotine, Jean-Jacques (2015). "Network motifs emerge from interconnections that favour stability". Nature Physics 11 (10): 848–852. doi:10.1038/nphys3402. Bibcode: 2015NatPh..11..848A.
8. ↑ Anand, Kartik; Bianconi, Ginestra (2009). "Entropy Measures for Networks: Toward an Information Theory of Complex Topologies". Physical Review E 80 (4). doi:10.1103/physreve.80.045102. PMID 19905379. Bibcode: 2009PhRvE..80d5102A.
9. ↑ Wissner-Gross, A. D.; Freer, C. E. (2013). "Causal Entropic Forces". Phys. Rev. Lett. 110 (16). doi:10.1103/physrevlett.110.168702. PMID 23679649. Bibcode: 2013PhRvL.110p8702W.
10. ↑ Zhao, Kun; Bruinsma, Robijn; Mason, Thomas G. (2012). "Local Chiral Symmetry Breaking in Triatic Liquid Crystals". Nature Communications 3 (801): 801. doi:10.1038/ncomms1803. PMID 22549830. Bibcode: 2012NatCo...3..801Z.
11. ↑ Jun, Suckjoon; Mulde, Bela (2006). "Entropy-driven spatial organization of highly confined polymers: Lessons for the bacterial chromosome". PNAS 103 (33): 12388–12393. doi:10.1073/pnas.0605305103. PMID 16885211. Bibcode: 2006PNAS..10312388J.
12. ↑ Bianconi, Ginestra; Anand, Kartik (2009). "Entropy measures for networks: Toward an information theory of complex topologies". Physical Review E 80 (4). doi:10.1103/PhysRevE.80.045102. PMID 19905379. Bibcode: 2009PhRvE..80d5102A.

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