The significant digit law in statistical physics
AbstractThe occurrence of the nonzero leftmost digit, i.e., 1,2,…,9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford’s law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann–Gibbs (BG) distribution, the Fermi–Dirac (FD) distribution, and the Bose–Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around Benford’s distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus Benford’s law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford’s law, especially the mantissa distribution of data sets, are discussed.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 389 (2010)
Issue (Month): 16 ()
Contact details of provider:
Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
First digit law; Statistical physics; Mantissa distribution;
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- David E. Giles, 2012. "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications," Econometrics Working Papers 1201, Department of Economics, University of Victoria.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.