Natural networks as thermodynamic systems

Tuomo Hartonen, Arto Annila*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

27 Citations (Scopus)


Natural networks are considered as thermodynamic systems that evolve from one state to another by consuming free energy. The least-time consumption of free energy is found to result in ubiquitous scale-free characteristics. The network evolution will yield the scale-independent qualities because the least-time imperative will prefer attachment of nodes that contribute most to the free-energy consumption. The analysis of evolutionary equation of motion, derived from statistical physics of open systems, reveals that evolution of natural networks is a path-dependent and nondeterministic process. Despite the noncomputability of evolution, many mathematical models of networks can be recognized as approximations of the least-time process as well as many measures of networks can be appreciated as practical assessments of the system's thermodynamic status.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
Issue number2
Publication statusPublished - Nov 2012
MoE publication typeA1 Journal article-refereed


  • Entropy
  • Evolution
  • Free energy
  • Natural process
  • Noncomputable
  • Power law scaling
  • Scale-free
  • Statistical mechanics
  • The principle of least action


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