James Clerk Maxwell, the Scottish scientist known for his pioneering work in the theory of electromagnetism, was also involved in developing the field of thermodynamics in the 19th century. His work and ideas provided insight into the microscopic phenomenon that give rise to the laws of thermodynamics. However, one such idea of his left scientists perplexed for more than a century. So much so that Lord Kelvin went as far as to associate the word ‘demon’ with it!
The notion of entropy is essential here – it is the measure of disorder of any system and by the second law of thermodynamics, entropy always increases with time. In other words, energy needs to be expended in order to keep disorder in check. Hence, left to itself, any system will proceed to a state of disorder from order.
Now, let us proceed to the actual details of the thought experiment. Think of a large room with a partition in the middle. The room is inhabited by a large family of rabbits, each running around at different speeds. The partition is fitted with a gate, which is guarded by Little Lucifer. His job is to let across only those rabbits which are running faster than a particular speed. Eventually, what happens is that rabbits faster moving rabbits end up in one half of the room, while the slower ones end up on the other. What this means is that there is an ordering of elements in the room resulting in a decrease of entropy (of course, the original experiment involved gas molecules instead of rabbits, but you get the picture).
On the face of it, this seems to violate the Second Law of Thermodynamics. But not so. Consider this analogy. Imagine an auditorium with a clean stage and curtains closed. A perfect setting save for the chairs which have been haphazardly scattered across the room. Being a Good Samaritan, you enter the hall and painstakingly arrange the chairs in a square matrix. The auditorium is now in a state of perfect order.
What this analogy helps with, and the previous one doesn’t, is that it becomes clear that the Good Samaritan here is expending energy. He transfers energy to the floor due to the friction from his shoes. Due to his body heat, he emits infrared radiation. These processes and numerous others increase the entropy of the system overall. A similar logic applies to the thought experiment that is Maxwell’s Demon – a demon controlling the middle partition of a closed gas chamber allowing only fast particles to pass through from one side and only slow particles from another. The demon creates a temperature difference on the two sides of the chamber with no expenditure of energy, apparently violating the laws of thermodynamics.
Two scientists, Rolf Landauer and Charles Bennett in the 1970s argued that the demon would have to measure the speed of particles to determine whether or not to allow it to pass through the partition. Each measurement is a unit of information and they concluded that after a period of time, the demon would run out of information storage space and have to delete old memory. The process of deletion requires a finite amount of energy and this increases the overall entropy of the system.
Although “the measure of disorder” is a compact way to explain entropy, it is not the complete explanation and leads to contradictions in numerous cases. Entropy is a measure of the number of ways to arrange the particles in system and generally, there is a higher proportion of disordered arrangements than ordered arrangements. However, a system can be cleverly designed such that there are more ordered arrangements than disordered ones. The formation of silicon crystals from the disordered gas phase on the surface of a metal catalyst is one such example. Apparently, the entropy seems to decrease due to the ordered nature of the silicon crystals. However, the release of energy due to bond formation increases the entropy of the system by an even greater amount.
For further reading about Maxwell’s Demon: https://www.britannica.com/science/Maxwells-demon