WINLAB 20201 Summer Internship
Overview of Maxwell's Demon
Maxwell’s Demon is a thought experiment that was proposed by James Clerk Maxwell in 1867. This experiment would hypothetically violate the second law of thermodynamics, which states that the entropy of a system has a natural tendency to always increase. Since entropy is a measure of disorder and randomness, this means that the system will grow more disordered and random. Maxwell’s thought experiment consists of two chambers of gas, separated by a demon-controlled door. Each chamber would have “hot” particlesーthose with high velocityーand “cold” particlesーthose with low velocity. As the particles would move around and approach the door, the demon would open the door for selected particles. Specifically, fast particles would be allowed to pass from side A to side B, and slow particles would be allowed to pass from side B to side A. Essentially, the demon would be controlling the door to sort all the fast particles to one side and all the slow particles to the other, creating one “hot” chamber and one “cold” chamber. Thus, most of the energy from the two chambers would be transferred to the "hot" chamber. If such a scenario were to occur, then the entropy of the entire system would be decreasing, as the particles would become more ordered. This, of course, violates the second law of thermodynamics, making this an extremely intriguing thought experiment.
Image for Maxwell's Demon
Overview of High Pressure Demon
Image for High Pressure Demon
The High Pressure Demon is a demon theorized by Professor Martin. This demon consists of a container of water, a plug, a rope, and deflectors. The plug hangs from the ceiling of the container via a rope, and floats at the top of the container when it is light. This is because the water molecules collide with the bottom of the plug, translating some of their kinetic energy to the plug and increasing the plug’s upward velocity. However, when the plug becomes heavier, these collisions are no longer able to keep the plug afloat. This is where the demon-controlled deflectors, which line the bottom of the container, come into play. When a water molecule hits a deflector, the demon rotates the deflector to redirect the particle towards the bottom of the plug. Thus, the number of particle-plug collisions increases alongside the amount of kinetic energy transferred from the particles to the plug, allowing the plug to stay suspended for heavier weights.
Overview of a simulation
In our coded simulations, we treat the demon and the world as two bodies that communicate with each other. Specifically, the world sends the position and velocity of each particle to the demon. Using the information it receives, the demon makes the decision to open or close the door in Maxwell’s Demon or rotate a deflector in High Pressure Demon. With this setup, we are able to implement bit error on the communication between the demon and the world and observe the consequences on the demon’s effectiveness in transferring energy.
Overview of information theory
Since a large focus of our project was communications and information transfer, we had to have a strong conceptual background in this area. To gain this knowledge, we studied Claude E. Shannon’s “A Mathematical Theory of Communication”, which introduces many concepts that are the backbone of modern-day information theory. The core concept that we used was Shannon’s version of information.
Shannon believes that the information carried by a message depends on the likelihood of that message occurring. For instance, if there is a 90% chance of rain and a 10% chance of sunshine, the message “It will rain” does not carry much information ー you already expect it to rain based on the forecast, so this message is just conformation. However, the message “It will be sunny” carries much more information since you expect it to rain, so learning that it will not rain provides a lot of value. Thus, given that the probability of a certain message occurring is p, Shannon formulated that the information carried by that message is log2(1/p). Using this formulation, we are able to monitor the total amount of information sent between the world and the demon in our simulation.
Poster for our project
