< theory > A measure of the disorder of a system. Systems tend to go from a state of order (low entropy) to a state of maximum disorder (high entropy).
The entropy of a system is related to the amount of information it contains. A highly ordered system can be described using fewer bit s of information than a disordered one. For example, a string containing one million "0"s can be described using run-length encoding as [("0", 1000000)] whereas a string of random symbols (e.g. bits, or characters) will be much harder, if not impossible, to compress in this way.
Shannon 's formula gives the entropy H(M) of a message M in bits:
H(M) = -log2 p(M)
Where p(M) is the probability of message M.