Does Maxwell's Demon Defy the Law of Entropy?

Talk to Arvin on Patreon: https://www.patreon.com/arvinash REFERENCES How can life arise from increasing entropy? https://youtu.be/CkAPhZ2QMg4 The link between entropy, time and information: https://youtu.be/T6CxT4AESCQ Why does entropy and time only go in one direction? https://youtu.be/pvPxCtrXT1c CHAPTERS 0:00 A universe of energy and information 1:30 Second law of thermodynamics 2:45 Boltzmann's equation of entropy 3:56 Maxwell's demon thought experiment 5:28 How was entropy decreased by Maxwell's demon 7:05 How the second law is not violated by the demon 8:07 Landauer's principle 10:31 How Maxwell's demon affects modern computers SUMMARY In this video, we’re exploring the link between information and entropy, by examining a famous thought experiments by James Clerk Maxwell, called Maxwell's demon, which seems to show that entropy can be reversed. In answering whether it really can, German physicist, Rolf Landauer discovered a surprising insight about information, which has huge implications for the computers we use today, and sets a limit of how powerful we can make them in the future. The second law of thermodynamics states that in a closed system, the total entropy always increases or remains constant in any spontaneous process. It never decreases. But what is entropy? it's not exactly the measure of disorder of a system. A better definition is the amount of information needed to describe a system. What does this mean? In the 19th century, Austrian physicist Ludwig Boltzmann found a formula, the Boltzmann equation, that showed how entropy of a system is related to the number of ways that the system’s particles can be arranged. The more ways that the particles of a system can be arranged, the higher the entropy of that system, and the higher the information required to describe the system. The more information that’s necessary, the higher the entropy. A system with high entropy has many possible arrangements, so describing its exact state requires more information. #entropy #computing Scottish Scientist James Clerk Maxwell questioned the absolute nature of the Second Law of Thermodynamics. Maxwell regarded entropy as a statistical phenomenon, not strictly required to always increase. In 1867 he devised a thought experiment to test how fundamental the second law of thermodynamics truly is, called Maxwell's Demon. He imagined a box divided into two halves by a sealed wall, with a tiny frictionless door large enough for a single molecule to pass through. Initially the two halves are in thermal equilibrium, representing maximum entropy of the gas. Maxwell's Demon is able to sort fast-moving and slow-moving gas molecules though the door, such that he's able to place all the slow moving molecules on one side of the door and all the fast moving ones on the other side. Since velocity of the gas particles corresponds to the temperature of the chambers, one side would be hotter than the other. Overall energy has not changed. But the entropy of the system has decreased. It has decreased because Initially, since the average kinetic energy of the atoms was evenly distributed, there were a greater number of ways to distribute the atoms’ energies and positions across the full volume of the chamber. But when the atoms with the same overall energy, are confined into two smaller volumes at different temperatures, this limits different combinations of speeds and positions that the atoms can take, resulting in a lower number of microstates, meaning lower entropy. In fact, Hungarian physicist Leó Szilárd proposed that one could harness this temperature difference to run a heat engine creating work. This outcome appears to contradict the second law of thermodynamics, because entropy seems to have decreased. Could this be correct? The answer turns out to be no, because in order for this to work, the demon has to process information in his brain in order to sort the atoms. This requires increasing information in his brain. The randomness of the particles in the box has decreased after they are sorted. But this randomness is not eliminated. It is merely transferred into the demon’s memory. In 1961, physicist Rolf Landauer showed that the entropy increase does not occur in the storage of information, but in its erasure. Erasing information creates heat. The energy cost of erasing information is given by Landauer's principle, which applies to all computational processes, including modern computers. What this means for modern computers is that every time a bit is erased, an energy cost has to be paid. This leads to a significant thermodynamic challenge in computing. It sets a theoretical minimum amount of energy required to erase a single bit of information. So we can't miniaturize components infinitely because we have to get rid of the heat. This is known as the Landauer Limit. Reversible computers and quantum computers may be able to use reversible computing to overcome this limit.