Generalized measurement of uncertainty and the maximizable entropy
Abstract
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation, bar(x)=sum(i)g(pi)xi, and the expression of dI, we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g(pi) may have different forms for different statistics which includes the extensive and nonextensive statistics.
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