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Keywords:

  • entropy;
  • evolution;
  • free energy;
  • natural process;
  • noncomputable;
  • power law scaling;
  • scale-free;
  • statistical mechanics;
  • the principle of least action

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. © 2012 Wiley Periodicals, Inc. Complexity, 2012