Page 251 - Becoming Metric Wise

242 Becoming Metric-Wise

7.14 PRATHAP’S THERMODYNAMIC INDICATORS

Prathap (2011a,b, 2014), proposed a series of indicators, which he
describes in a thermodynamic framework. We will not go into details but
just give their definitions.
Consider a set of P publications and their respective numbers of cita-
tions (c k ) k51,.. .,P during a given citation window. Then the number of
publications, P, can be written as:
P
X 0
P 5 c k ðÞ (7.35)
k51
The total number of received citations is then:
P
X 1
C 5 c k ðÞ (7.36)
k51
It is then natural to introduce a second-order indicator:
P
X
E 5 c k ðÞ 2 (7.37)
k51
which is called the energy.
If the impact is denoted as i, then
C
i 5 (7.38)
P
Next Prathap introduces the so-called exergy, denoted as X, and
defined as:
C 2
2
X 5 i P 5 5 iC (7.39)
P
The entropy of the system is then defined as S 5 E 2 X. Finally, he
introduces the notion of consistency, denoted as ν, and defined as:
X
ν 5 (7.40)
E
Prathap (2014) argues that besides quantity (P)and quality(C) a third
attribute, namely consistency (7.40) must be considered for a complete three-
dimensional evaluation of a research portfolio. Consistency can be interpreted
as the variation in the quality of the portfolio. Indeed, if ν is equal to one,
then X 5 E andall papers in theset have thesamenumber ofcitations.