Article(id=1242120598063748027, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242120596776096697, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1272902400000, receivedDateStr=2010-05-04, revisedDate=-2209017600000, revisedDateStr=1900-01-01, acceptedDate=null, acceptedDateStr=null, onlineDate=1285603200000, onlineDateStr=2010-09-28, pubDate=1285603200000, pubDateStr=2010-09-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1285603200000, onlineIssueDateStr=2010-09-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774074228060, creator=sys-migrate, updateTime=1774074228060, updator=sys-migrate, issue=Issue{id=1242120596776096697, tenantId=1146029695717560320, journalId=1146031591421210625, year='2010', volume='28', issue='18', pageStart='3', pageEnd='140', issueExtLink='null', onlineDate='null', pubDate='1285603200000', pubDateStr='2010-09-28', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774074227753, creator='sys-migrate', updateTime=1774074227753, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=98, endPage=102, ext={EN=ArticleExt(id=1242120604623639513, articleId=1242120598063748027, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=Applications of the First Digit Law in Physics, columnId=1242116810380743325, journalTitle=Science & Technology Review, columnName=Reviews, runingTitle=null, highlight=null, articleAbstract=The 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. This paper discusses systematically the first digit distributions of physical quantities in the fields of particle physics and astrophysics, and it is found that the full widths of hadrons and various quantities of pulsars conform to Benford's law very well. The first and second digit distributions of derivatives of period and frequency of pulsars are also found to obey the n-digit Benford's law. It is further pointed out that the pulsar data can serve as an ideal assemblage to study the first digit distributions of the real world data. Furthermore, three kinds of widely used physical statistics, i.e., the Boltzmann-Gibbs distribution, the Fermi-Dirac distribution, and the Bose-Einstein distribution, are found to conform to this law in an analytical manner. Thus, a new physical prospective is used to look into the underlying reason of this law. Moreover, various elegant mathematical properties of Benford's law are discussed in detail., authors=null, authorsList=null, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=Bo-Qiang Ma, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=h2n+f4c19AcEsMXrGsZ3xw==, pdfFileSize=1010582, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242120602857837516, articleId=1242120598063748027, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=首位数规律在物理学中的应用, columnId=1242116809164390686, journalTitle=科技导报, columnName=综述文章, runingTitle=null, highlight=null, articleAbstract=自然世界数据库中的首位非零数字并不以1~9的等概率出现，而是符合一个对数分布，即Benford定理。在研究该定理在粒子物理与天体物理中的表现时发现，粒子物理中的强子宽度与寿命、脉冲星中的功率与运动等多类物理量均符合Benford分布；统计物理中的三大正则统计——玻尔兹曼-吉布斯统计、费米-狄拉克统计和玻色-爱因斯坦统计均解析满足首位数规律。本文简介了首位数定理，阐述了其在粒子物理、脉冲星中的应用，讨论其标度不变性、整数幂次不变性、基数不变性等性质，最后分析了三大物理统计中的首位数规律。如何更好地理解Benford定理这个“百年难题”，探讨首位数分布的自然规律，还需要更多的后续研究。, authors=邵立晶,马伯强, authorsList=邵立晶;马伯强, authorCompany=北京大学物理学院；核物理与核技术国家重点实验室，北京 100871, correspAuthors=null, authorNote=null, correspAuthorsNote=马伯强, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=xmEOMw5x1DuRFRkobE4nEQ==, pdfFileSize=1010582, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null)}, authors=null, keywords=[Keyword(id=1242120602438402903, tenantId=1146029695717560320, journalId=1146031591421210625, 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