We presented background information about various entropies in theliterature. The pathway idea of Mathai (2005) is shown to be inferable from themaximization of a certain generalized entropy measure and establishedconnections to outstanding problems in astronomy and physics. In this paper weproved that the generalized entropy of Mathai associated with diffusiveprocesses grows linearly with the logarithm of time, and the rate of growth isindepen- dent of the generalized entropy parameter. We also proposed someresults concerning images of generalized Bessel function under the pathwayoperator and its special cases including some trigonometric functions.Situations are listed where a generalized entropy of order ? leads to pathwaymodels, exponential and power law behavior and related differential equations.
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