Fisher information and the thermodynamics of scale-invariant systems

A. Hernando, C. Vesperinas and A. Plastino

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 3, 490-498

Abstract: 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.

Keywords: Fisher information; Scale-invariance (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:3:p:490-498

DOI: 10.1016/j.physa.2009.09.054

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