":Ywaz - you said: 

 PAR: "" what you call ""Objective Entropy"" is not entropy, it is the amount of information in a particular message (microstate), "" 
 Don't you mean entropy = information in a Macrostate? That is what you should have said. 

 :What I said was ""what you call ""Objective Entropy"" (given in your equation above) is not entropy, it is the amount of information in a particular message (microstate), assuming independence, and assuming that the frequencies of the symbols in the message are a perfect indication of the frequencies of the population (macrostate) from which it is drawn."" 

 :Entropy is the AVERAGE amount of MISSING information in a macrostate. It is the AVERAGE amount of information SUPPLIED by knowing a microstate. 

 :Assuming the probability of the i-th microstate is pi, and assuming they are independent,  the information supplied by knowing the i-th microstate is -log2(pi) bits. The entropy is the weighted average: It is the sum over all i of -pi log2(pi) (bits). Note that the sum over all i of pi is unity.    

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