4 - Entropy

Summary

The concept of entropy is central to information theory (IT). The name, of Greek origin (entropia, tropos), means turning point or transformation. It was first coined in 1864 by the physicist R. Clausius, who postulated the second law of thermodynamics. Among other implications, this law establishes the impossibility of perpetual motion, and also that the entropy of a thermally isolated system (such as our Universe) can only increase. Because of its universal implications and its conceptual subtlety, the word entropy has always been enshrouded in some mystery, even, as today, to large and educated audiences.

The subsequent works of L. Boltzmann, which set the grounds of statistical mechanics, made it possible to provide further clarifications of the definition of entropy, as a natural measure of disorder. The precursors and founders of the later information theory (L. Szilárd, H. Nyquist, R. Hartley, J. von Neumann, C. Shannon, E. Jaynes, and L. Brillouin) drew as many parallels between the measure of information (the uncertainty in communication-source messages) and physical entropy (the disorder or chaos within material systems). Comparing information with disorder is not at all intuitive. This is because information (as we conceive it) is pretty much the conceptual opposite of disorder! Even more striking is the fact that the respective formulations for entropy that have been successively made in physics and IT happen to match exactly. A legend has it that Shannon chose the word “entropy” from the following advice of his colleague von Neumann: “Call it entropy.