Fisher-information and the thermodynamics of scale-invariant systems

Abstract

We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and fluids is seen to emerge in natural fashion. We focus 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.

References in corpus (5)

• Critical Behavior in Light Nuclear Systems: Experimental Aspects
• Empirical Tests of Zipf's law Mechanism In Open Source Linux Distribution
• Competitive cluster growth in complex networks
• Zipf's law in Nuclear Multifragmentation and Percolation Theory
• Unravelling the size distribution of social groups with information theory on complex networks

Cited by in corpus (8)

• The workings of the Maximum Entropy Principle in collective human behavior
• Space-time correlations in urban sprawl
• MaxEnt and dynamical information
• The thermodynamics of urban population flows
• Inferring an optimal Fisher measure
• Memory endowed US cities and their demographic interactions
• Variational Principle underlying Scale Invariant Social Systems
• Unravelling the size distribution of social groups with information theory on complex networks