Fisher-information and the thermodynamics of scale-invariant systems
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 foc...
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| Veröffentlicht in: | arXiv.org 2009-08 |
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| creator | Hernando, A Vesperinas, C Plastino, A |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.0908.0504 |
| format | Article |
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| subjects | Computational fluid dynamics Computer simulation Fisher information Ideal gas Invariants Physics - Data Analysis, Statistics and Probability Physics - Physics and Society Thermodynamic properties Zipf's Law |
| title | Fisher-information and the thermodynamics of scale-invariant systems |
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