Thermodynamic cost of computation, algorithmic complexity and the information metric

Algorithmic complexity is a measure of randomness. In contrast to Shannon's entropy it is defined without a recourse to probabilities; for a binary string s it is given by the size, in bits, of the shortest computer program with the output s. I show that algorithmic complexity sets limits on the thermodynamic cost of computations, casts a new light on the limitations of Maxwell's demon and can be used to define distance between binary strings.

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