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Information Storage

Nucleic acids, particularly DNA, store and transmit genetic information, a foundational concept in molecular biology.
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The statement of the theorem

Let SS be a sequence of length LL, and let P(si)P(s_i) be the probability of finding nucleotide sis_i at position ii. The information content I(S)I(S) stored in the sequence, measured in bits, is defined by the Shannon entropy HH: \nH(S)=−∑s∈ΣP(s)log⁡2P(s)H(S) = -\sum_{s \in \Sigma} P(s) \log_2 P(s) \nFor a sequence generated by a Markov process of order kk, the conditional probability P(si∣si−k,…,si−1)P(s_i | s_{i-k}, \dots, s_{i-1}) governs the sequence generation, and the total information is related to the joint probability distribution P(S)=∏i=1LP(si∣si−k,…,si−1)P(S) = \prod_{i=1}^{L} P(s_i | s_{i-k}, \dots, s_{i-1}).
Source: Wikipedia