Renyi entropy

Generalized Renyi Entropies and Dimensions A hierarchy of generalized entropies and dimensions, SQ B,t), s[ B,t), S B,t),. .. - analogous to the hierarchy of fractal dimensions, Dq, Di,. .., introduced earlier in equation 4.94 for continuous systems may also be defined ... 

Other entropy types have been developed to determine the mixing level in systems, including Shannon entropy and Renyi entropy. Shannon entropy has been used to show distributive mixing levels in color mixing experiments [18,19], while Renyi entropy has been used to show a more rigorous analysis of distributive mixing [20, 21]. The reader is referred to the references as these types of entropies are beyond the scope of this chapter. 

Wang, W., Manas-Zloczower, I., and Kaufman, M., Characterization of Distributive Mixing in Polymer Processing Equipment using Renyi Entropies, Int. Polym. Process., 16, 315 (2001)... 

A full analytical solution of the cross channel flow vx(x,y) and vy x, y), for an incompressible, isothermal Newtonian fluid, was presented recently by Kaufman (18), in his study of Renyi entropies (Section 7.4) for characterizing advection and mixing in screw channels. The velocity profiles are expressed in terms of infinite series similar in form to Eq. 6.3-17 below. The resulting vector field for a channel with an aspect ratio of 5 is shown... 

Renyi (78) generalized the concept of information entropy to measure different aspects of system homogeneity, and Alemanskin et al. (79), and Alemanskin and Manas-Zloczower (80) adopted the Renyi entropy for measuring mixing. Considering only statistically independent partition, Renyi determined that the information entropy can be replaced with the following single-variable function... 

Linear a number of entropies, dimensions, Renyi measures, multi-fractal and fractal measures, and surrogate based quantities, iii. Prediction... 

Parvan A S, Biro T S. Extensive Renyi statistics from non-extensive entropy. Phys. Lett. A. 2005 340(5-6) 375-387. 

Renyi, A., Some fundamental questions of information theory, MTA III Oszt. Kdzl., 10, 251, 1960 On measures of information and entropy, in Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability, Berkeley University Rress, Berkeley, CA, 1960, 547 Probability Theory, North Holland, Amsterdam, 1970. 

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