Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.
Proc Natl Acad Sci U S A. 1981 Dec;78(12):7839-43. doi: 10.1073/pnas.78.12.7839.
The entropy function H = -Sigmap(j) log p(j) (p(j) being the probability of a system being in state j) and its continuum analogue H = integralp(x) log p(x) dx are fundamental in Shannon's theory of information transfer in communication systems. It is here shown that the discrete form of H also appears naturally in single-lane traffic flow theory. In merchandising, goods flow from a whole-saler through a retailer to a customer. Certain features of the process may be deduced from price distribution functions derived from Sears Roebuck and Company catalogues. It is found that the dispersion in logarithm of catalogue prices of a given year has remained about constant, independently of the year, for over 75 years. From this it may be inferred that the continuum entropy function for the variable logarithm of price had inadvertently, through Sears Roebuck policies, been maximized for that firm subject to the observed dispersion.
熵函数 H = -Sigmap(j) log p(j)（p(j) 是系统处于状态 j 的概率）及其连续体类似物 H = integralp(x) log p(x) dx 在香农的通信系统信息传输理论中是基本的。这里表明，H 的离散形式也自然出现在单车道交通流理论中。在商品销售中，货物从批发商流向零售商，再流向顾客。从西尔斯罗巴克公司的目录中得出的价格分布函数可以推导出该过程的某些特征。研究发现，给定年份的目录价格对数的离散度在 75 年以上的时间里几乎保持不变，与年份无关。由此可以推断，西尔斯罗巴克公司的价格对数连续熵函数在观察到的离散度下，通过西尔斯罗巴克公司的政策，无意中被最大化了。
