Significance of Maxwell’s Demon for the understanding of Entropy, Information and Time

Significance of Maxwell’s Demon for the understanding of Entropy, Information and Time

As far as our understanding of the Universe goes, all the physical laws that govern Nature are time-reversible except for the Second Law of Thermodynamics which states that the change in entropy in an isolated system can never decrease ( ΔS≥0) , which makes it appear time irreversible as going back in time would mean decreasing the entropy of the closed system and hence violating the second law of thermodynamics. Imagine cracking an egg, once cracked for it to reseal itself it would have to decrease in entropy and go back in time without any external forces if modeled as a closed system.

What causes entropy to increase?

If we model a rigid body such as a crate with a barrier in the middle, half of the crate is filled with a gas and the other half is a vacuum. On removing the barrier, we increase the volume that the gas fills as gasses are known to expand into the shape of their container; this results in an increase in entropy because now there are more ways to describe the microstates of the system, meaning that there more possible arrangements of gas molecules within a larger volume then a smaller one, which was proved by Ludwig Boltzmann with his equation for entropy, which is interestingly carved on his tombstone, S=klogW ( where k is Boltzmann’s constant and W is the number of real microstates). You would think that if we compressed the gas back to its original volume, we would decrease entropy and hence violate the second law of thermodynamics. However, compressing the gas requires external work to be done, which in turn increases the temperature of the system and increase the kinetic energy of the gas molecules, so that there are now more ways to describe the dynamics of the molecules compared to a cooler system, which results in an increase in entropy.

In 1867, James Clerk Maxwell, who is known for his theory of electromagnetism, devised a thought experiment, which was later known as Maxwell’s demon. To understand this brilliant experiment, once again imagine our crate but this time the barrier has a frictionless door on it that opens and closes to let molecules go through. At first, the door is open until the gas molecules spread out evenly on both sides of the door. Now imagine a demon that controls when the door opens and closes and only opens the door so that the molecules only travel into one half of the box and not back into the other. This would result in a decrease of entropy, as no external work is being done, and a violation of the second law of thermodynamics. This seemed completely plausible and was a mystery for more than 100 years.

In 1982 Rolf Landauer and Charles Benneth solved this problem by proving that in order for the demon to know when to open the door to reduce entropy he has to gather information about the motion of the molecules, which in turn increases the entropy inside his brain. Following this ground-breaking discovery, they proved that the increase in entropy in the demon’s brain counterbalances the decrease of the entropy of the gas molecules as the demon is part of the system . Moreover , scientists argued that you can just erase the demon’s memory but Benneth and Landauer proved that erasing information requires external work, leading to an increase in heat and entropy and hence obeying the second law of thermodynamics. This discovery redefined entropy as the information required to describe all the microstates of a system, meaning that if entropy was decreasing we would not have memories and consciousness.

What does time have to do with entropy?

An astronomer Arthur Eddington hypothesized that the increase in entropy was responsible for the increase for the forward flow of time as the second law of thermodynamics is time irreversible just like the flow of time? This is because the entropy of the universe tends to increase as the volume of the Universe is constantly expanding at an accelerating rate and hence there are more ways for molecules to arrange themselves in the future than in the present just like a chessboard with game pieces. However, for now, this is just a theory and it is not known for certain what causes forward time flow.

Can we violate the second law of thermodynamics?

Yes, however it is extremely improbable. Imagine our rigid box but this time with no barrier, the gas molecules can arrange themselves so that they all are on one half of the box. So, therefore, we have not inputted any extra work into the system to produce heat and we do not need information on the motion of molecules, which means that the entropy has spontaneously decreased, violating the second law of thermodynamics. However, the chance of this is 1 in 10^150,000,000,000,000,000,000,000, leading to the fact that the second law of thermodynamics must be a statistical law and not absolute! Continuing with Eddington’s postulate, does this mean that backward flow of time is also not impossible but just extremely improbable?