## Abstract

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 language | English |
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Pages (from-to) | 53-62 |

Number of pages | 10 |

Journal | Complexity |

Volume | 18 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 2012 |

MoE publication type | A1 Journal article-refereed |

## Keywords

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