Citation entropy and research impact estimation

A new indicator, a real valued s-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious h-index, at the same time avoiding some its obvious drawbacks. Sound, sound your trumpets and beat your drums! Here it is, an impossible thing performed: a single integer number characterizes both productivity and quality of a scientific research output. Suggested by Jorge Hirsch [1], this simple and intuitively appealing h-index has shaken academia like a storm, generating a huge public interest and a A Russian physicist with whom I was acquainted long ago used to say that the academia is not a Christian environment. It is a pagan one, with its hero-worship tradition. But hero-worshiping requires ranking. And a simple indicator, as simple as to be understandable even by dummies, is an ideal instrument for such a ranking. h-index is defined as given by the highest number of papers which has received h or more citations. Empirically, h = C tot a , (1) with a ranging between three and five [1]. Here C tot stands for the total number of citations. And now, with this simple and adorable instrument of ranking on the pedestal, I'm going into a risky business to suggest an alternative to it. Am I reckless? Not quite. I know a magic word which should impress pagans with an irresistible witchery. Claude Shannon introduced the quantity S = − N i=1 p i log p i , (2) which is a measure of information uncertainty and plays a central role in information theory [12]. On the advice of John Von Neumann, Shannon called it entropy. According to Feynman [13], Von Neumann declared to Shannon that this magic word would give him " a great edge in debates because nobody really knows what entropy is anyway ". Armed with this magic word, entropy, we have some chance to overthrow the present idol. So, let us try it! Citation entropy is naturally defined by (2), with p i = C i C tot , where C i is the number of citations on the i-th paper of the citation series. Now, in analogy with (1), we can define the citation record strength index, or s-index, as follows s = 1 2 SC tot S 0 , (3) where S 0 = log N is the maximum …