Dynamic shear localization attracted interest as both experimental and theoretical evidence suggested that its origins are not only due, as believed, to thermal softening, but are most likely related to microstructural evolutions, the latter being driven by a critical value of the stored strain energy. Yet, nothing is known about the effects of the distribution (heterogeneity) of this stored energy at the microstructural level. Using the well-known concept of Shannons entropy, we systematically compare different heterogeneities, and conclude that small amounts of microstructural heterogeneity may significantly influence shear localization, as opposed to larger values of homogeneously distributed strain energy