Complexity_ A Guided Tour - Melanie Mitchell [23]
Szilard’s theory was later extended and generalized by the French physicists Leon Brillouin and Denis Gabor. Many scientists of the 1950s and later believed that Brillouin’s theory in particular had definitively finished off the demon by demonstrating in detail how making a measurement entails an increase of entropy.
However, it wasn’t over yet. Fifty years after Szilard’s paper, it was discovered that there were some holes in Szilard’s and Brillouin’s solutions as well. In the 1980s, the mathematician Charles Bennett showed that there are very clever ways to observe and remember information—in the demon’s case, whether an air molecule is fast or slow—without increasing entropy. Bennett’s remarkable demonstration of this formed the basis for reversible computing, which says that, in theory, any computation can be done without expending energy. Bennett’s discoveries might seem to imply that we are back at square one with the demon, since measurement can, in fact, be done without increasing entropy. However, Bennett noted that the second law of thermodynamics was saved again by an earlier discovery made in the 1960s by physicist Rolf Landauer: it is not the act of measurement, but rather the act of erasing memory that necessarily increases entropy. Erasing memory is not reversible; if there is true erasure, then once the information is gone, it cannot be restored without additional measurement. Bennett showed that for the demon to work, its memory must be erased at some point, and when it is, the physical act of this erasure will produce heat, thus increasing entropy by an amount exactly equal to the amount entropy was decreased by the demon’s sorting actions.
Landauer and Bennett’s solution to the paradox of Maxwell’s demon fixed holes in Szilard’s solution, but it was in the same spirit: the demon’s act of measurement and decision making, which requires erasure, will inevitably increase entropy, and the second law is saved. (I should say here that there are still some physicists who don’t buy the Landauer and Bennett solution; the demon remains controversial to this day.)
Maxwell invented his demon as a simple thought experiment to demonstrate his view that the second law of thermodynamics was not a law but a statistical effect. However, like many of the best thought-experiments in science, the demon’s influence was much broader: resolutions to the demon paradox became the foundations of two new fields: information theory and the physics of information.
Statistical Mechanics in a Nutshell
In an earlier section, I defined “entropy” as a measure of the energy that cannot be converted into additional work but is instead transformed into heat. This notion of entropy was originally defined by Rudolph Clausius in 1865. At the time of Clausius, heat was believed to be a kind of fluid that could move from one system to another, and temperature was a property of a system that affected the flow of heat.
In the next few decades, a different view of heat emerged in the scientific community: systems are made up of molecules, and heat is a result of the motion, or kinetic energy, of those molecules. This new view was largely a result of the work of Ludwig Boltzmann, who developed what is now called statistical mechanics.
Ludwig Boltzmann, 1844–1906 (AIP Emilio Segre Visual Archives, Segre Collection)
Statistical mechanics proposes that large-scale properties (e.g., heat) emerge from microscopic properties (e.g., the motions of trillions of molecules). For example, think about a room full of moving air molecules. A classical mechanics analysis would determine the position and velocity of each molecule, as well as all the forces acting on that molecule, and would use this information to determine the future position and velocity of that molecule. Of course, if