4 ms·
Is that the same as H'=-\sum _{i=1}^{R}p_{i}\ln p_{i} as per https://en.wikipedia.org/wiki/Diversity_index#Shannon_index https://en.wikipedia.org/wiki/Diversi
by tingletech 7y ago
Is that the same as
H'=-\sum _{i=1}^{R}p_{i}\ln p_{i}
as per https://en.wikipedia.org/wiki/Diversity_index#Shannon_index https://en.wikipedia.org/wiki/Diversity_index#Shannon_index
With a log base e for nits (or natural digits) and a log base 2 for bits (or binary digits) as per _a mathematical theory of communication_ (Shannon 1948)?
- c1ccccc1 7y agoNot quite. The formula you gave is the more general one, the previous one assumes that all microstates are equally likely. Given that assumption they are equivalent though.
- tingletech 7y agohow does one read "log #{microstates}"? Is it simply "log of the number of microstates"?
- foxes 7y agoYes.
- n4r9 7y agoThere's a quote by von Neumann advising Shannon on what to name his measure of uncertainty: > You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage.