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Fisher information and the thermodynamics of scale-invariant systems


  • Hernando, A.
  • Vesperinas, C.
  • Plastino, A.


We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of the Fisher information measure. In such a way a clear analogy between these systems’ thermal properties and those of gases and fluids is seen to emerge in a natural fashion. We focus our attention on the non-interacting scenario, speaking thus of scale-free ideal gases (SFIGs) and present some empirical evidences regarding such disparate systems as electoral results, city populations and total citations in Physics journals, that seem to indicate that SFIGs do exist. We also illustrate the way in which Zipf’s law can be understood in a thermodynamical context as the surface of a finite system. Finally, we derive an equivalent microscopic description of our systems which totally agrees with previous numerical simulations found in the literature.

Suggested Citation

  • Hernando, A. & Vesperinas, C. & Plastino, A., 2010. "Fisher information and the thermodynamics of scale-invariant systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 490-498.
  • Handle: RePEc:eee:phsmap:v:389:y:2010:i:3:p:490-498
    DOI: 10.1016/j.physa.2009.09.054

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    Cited by:

    1. Hawkins, Raymond J. & Aoki, Masanao & Roy Frieden, B., 2010. "Asymmetric information and macroeconomic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3565-3571.

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    Fisher information; Scale-invariance;


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