Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos

by Seth Lloyd

As the nineteenth century wound on, Boltzmann, Gibbs, and the German physicist Max Planck refined their formulas describing the energy and entropy of systems made up of atoms. In particular, they discovered that the entropy of a system was proportional to the number of bits required to describe the microscopic state of the atoms. This result was so useful in describing the trade-offs between heat and energy that the formula that encompasses it is inscribed on Boltzmann’s tomb. Entropy is traditionally written S, and the number of different possible microscopic states (or “complexions,” as Planck called them) is W. W could be the number of complexions of an individual atom or of a system made of atoms. The epitaph on Boltzmann’s tomb reads “S = k log W,” which is just a fancy way of saying that the entropy of something is proportional to the number of bits registered by its microscopic state. Another way of saying the same thing is that the entropy is proportional to the length, in bits, of the number of the microscopic states. In this formula, k is known as Boltzmann’s constant.