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May8-10, 01:01 PM
PF Gold
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P: 765
From: the physics arXiv Blog:

Benford's Law And A Theory of Everything

Today, Lijing Shao and Bo-Qiang Ma at Peking University in China provide a new insight into the nature of Benford's law. They examine how Benford's law applies to three kinds of statistical distributions widely used in physics.

These are: the Boltzmann-Gibbs distribution which is a probability measure used to describe the distribution of the states of a system; the Fermi-Dirac distribution which is a measure of the energies of single particles that obey the Pauli exclusion principle (ie fermions); and finally the Bose-Einstein distribution, a measure of the energies of single particles that do not obey the Pauli exclusion principle (ie bosons).
Lijing and Bo-Qiang say that the Boltzmann-Gibbs and Fermi-Dirac distributions distributions both fluctuate in a periodic manner around the Benford distribution with respect to the temperature of the system. The Bose Einstein distribution, on the other hand, conforms to benford's Law exactly whatever the temperature is.

What to make of this discovery? Lijing and Bo-Qiang say that logarithmic distributions are a general feature of statistical physics and so "might be a more fundamental principle behind the complexity of the nature".

That's an intriguing idea. Could it be that Benford's law hints at some kind underlying theory that governs the nature of many physical systems? Perhaps.

But what then of data sets that do not conform to Benford's law? Any decent explanation will need to explain why some data sets follow the law and others don't and it seems that Lijing and Bo-Qiang are as far as ever from this.
Anyone have an educated opinion/guess as to what that might be ? Highlighted in blue above...

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