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(p_i)x_i, and the expression of dI, we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g(p_i) may have different forms for different statistics which includes the extensive and nonextensive statistics.

11 pages

References in corpus (2)

• The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?
• A new expression of the probability distribution in incomplete statistics and fundamental thermodynamic relations