deletions | additions       diff --git a/Gibbs.tex b/Gibbs.tex  index fe8fead..208e193 100644  --- a/Gibbs.tex  +++ b/Gibbs.tex 
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When bits are written randomly and independently, the entropy of the source is given by  \begin{equation}  \label{eqn:indep_entropy}   H = -\sum_i p_i \log_2 p_i.  \label{eqn:indep_entropy}  \end{equation}  However, there may be larger-scale patterns in the string. Then we have to make more effort (WHY?). For example, \texttt{0101010101\cdots} has the same entropy as \texttt{010011000111\cdots}, but clearly there's something different going on! I see two cases, which have to be treated differently: