Maxwell’s demon is the name of a thought experiment that has been intensely discussed by physicists and philosophers investigating the relation between energy, information, and time. In this experiment, an imaginary but not supranatural being is using his extraordinary sensorial and intellectual powers to violate the second law of thermodynamics and, therefore, to falsify the fundamental principle by which modern physics explains the irreversible direction of time. The demon is named after one of the greatest physicists of all time, James Clerk Maxwell (1831-1879), who developed the theory of the electromagnetic field and conceived, in 1867, the experiment with the fictitious being.
The problem Maxwell wanted to solve by his thought experiment is whether a physical process might be conceived that, though being consistent with all known laws of physics, breaks the second law of thermodynamics. This law states that the entropy of a thermodynamically closed system never decreases so that it is possible to objectively measure the irreversible flow of time by comparing the entropy of different states of such a system. How did Maxwell suppose his demon to perform the feat of violating the second law? The demon, who has superhuman abilities but must act according to the laws of physics, is sitting in a closed container that is filled with gas and divided, by an impermeable partition, into two halves. In the partition there is a door that can be opened and closed at will. The demon observes the gas molecules approaching the door in both halves and sorts them by deciding which molecules are allowed to move through the door so that, for example, the faster ones will be gathered in the left half and the slower ones in the right half. Because the left half gradually becomes warmer and the right one cooler, the resultant temperature difference can be used to do work. Suppose that Maxwell’s demon and the door could operate in a reversible manner, giving up some amount of energy when opening the door without friction and taking in the same amount of energy when closing it without friction. Then the container would constitute, for all practical purposes, a perpetuum mobile that, thanks to the demon, could completely transform heat flowing from a reservoir at lower temperature to a reservoir at higher temperature into work.
Even a short description of Maxwell’s demon shows that information plays a crucial role in reasoning about the thought experiment. The demon must know the positions and the velocities of the molecules that are approaching the door to decide reasonably whether it is to be opened or closed. To bring order into a disordered system (thermodynamically speaking, to lower its entropy), information about the components of the system is needed. Therefore the physical nature of information must be taken into account if we want to find the weak spot of Maxwell’s demon and to show that the thought experiment is not a counterargument against the universal validity of the second law of thermodynamics. The history of the discussion about Maxwell’s demon mirrors the difficulties encountered in the development of a physics of information. Arguments for the possibility of Maxwell’s demon, and against it, revolved around the information-gathering activity of the imaginary being: How does the demon come to know the location and speed of single molecules, and is the thermodynamic cost of gathering this information high enough to rescue the second law of thermodynamics because it produces at least the same amount of entropy that it makes possible to consume?
In 1982, a quantum physicist and computer scientist, Charles H. Bennett, brought forth the conclusive argument against the possible existence of Maxwell’s demon. Bennett showed that it was not the gathering, as everyone had thought before, but the erasure of information that is decisive for an adequate understanding of the demon. The reason for this is that the demon needs a memory in which information about the molecules can be stored. Because the demon is, though fictitious, a physical being, this memory is finite. At some time the demon must begin to forget—that is, to erase information about the locations and velocities of molecules he has observed; otherwise, he could not memorize new information about molecules approaching the door. “Erasing information” means here that it is impossible for the demon to gather the deleted information once again. Bennett calls this kind of irreversibility that concerns the inability to infer a former state of a system from information about its given state, logical irreversibility.
Because different pieces of information must be represented by different physical states, logical irreversibility is combined with thermodynamic irreversibility. The higher the number of different equiprobable pieces of information a system can have, the higher its entropy is. Erasure of information thus decreases the entropy of the demon’s memory: At first, the memory unit containing the information could have been in a number of different equiprobable states (“molecule x is in state y at time t”); then the erasing process resets it to a predefined state (“unknown molecule is in unknown state at unknown time”). Because the erasure of information in the demon’s memory shall be logically irreversible, this process must emit an amount of heat into the environment of the demon that increases the environment’s entropy to a higher extent than the entropy of the demon’s memory is decreased. Bennett shows that this net increase at least counterbalances the decrease in the environment’s entropy that happens thanks to the information-gathering activities of Maxwell’s demon. Altogether, the entropy of the whole container is at best constant, and the second law of thermodynamics is rescued. By the power of information- theoretical and thermodynamical reasoning, Maxwell’s demon thus shows us that the irreversibility of time is the same as the loss of information that we, as finite beings, must inevitably experience.
See also Entropy; Experiments, Thought; Information;
Logical Depth; Time, Arrow of
Bennett, C. H. (1973). Logical reversibility of computing. IBM Journal of Research and Development, 17, 525-532.
Bennett, C. H. (1987). Demons, engines, and the second law. Scientific American, 257, 108-116.
Leff, H. S., & Rex, A. F. (Eds.). (2003). Maxwell’s demon 2: Entropy, classical and quantum information, computing. Philadelphia, PA: Institute of Physics.