Maxwell's demon

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Maxwell's demon is a thought experiment invented by James Maxwell, which can be found in his book[1]. In PKC, Maxwell's demon is abbreviated as MxD.

MxD as a Universal Construct

The simple thought experiment by James Maxwell very much resembles the characteristics of a quantum bit, or qubit. It consists of a device that has two possible states that cannot be immediately determined until some measurements is conducted. The ability to conduct this measurement without distorting the actual state of the system has been extensively discussed and studied, and resulted in major advances in quantum physics, and related to ideas such as information erasure. It was until the late 80s in the twentieth century, that Bennett and others cracked the puzzle for MxD, that it costs energy to extract information.

Proposition: Use Kan Extension to model MxD

Knowing that Kan Extension/Lift pair is the most universal of all universal constructs[2]. This assertion prompts us to map the concept of MxD to Kan Extension. While we are talking about universal constructs, it is necessary to mention that the concept covers not only classical logic, but also reversible logics[3]. Imagine how the demon is trying to figure out the position or energy distribution of two chambers, which can be most confounding if the two chambers are exactly alike and no differences between the two chambers can be told. Therefore, all the demon can do is to pray for god to help it tp break information symmetry. Just like a trader making a buy/sell decision in the market place, the basic notion of telling left/right, lift/extend, up/down, and other counter-balancing pairs of actions make symmetry, all primitive universal components must cope symmetry/symmetry-breaking at its core. The core is that all universal components must be some form of a symmetry breaking device.


References

  1. ↑ Maxwell, James (1871). Theory of Heat (PDF). local page: Longmans, Gree and Co. 
  2. ↑ Lehner, Marina (2014). "All Concepts are Kan Extensions":Kan Extensions as the Most Universal of the Universal Constructions (PDF) (Bachelor). local page: Harvard College. Retrieved June 28, 2021. 
  3. ↑ Reversible Logic

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