Variability as a better characterization of Shannon entropy

@article{Carcassi2021VariabilityAA,
  title={Variability as a better characterization of Shannon entropy},
  author={Gabriele Carcassi and Christine A. Aidala and Julian B. Barbour},
  journal={European Journal of Physics},
  year={2021},
  volume={42}
}
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and misunderstanding. We will show that the Shannon entropy can be fully understood as measuring the variability of the elements within a given distribution: it characterizes how much variation can be found within a collection of objects. We will see that it is… 
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