Let's consider a classical Maxwell demon as described in wiki https://en.wikipedia.org/wiki/Maxwell%27s_demon. It spends energy for measuring velocities and coordinates of some particles and uses the obtained information to create temperature difference between two parts of the container.
Then let's suppose that the demon doesn't use the information obtained by the measurements immediately but saves it into some information storage. So if the fraction of measured particles is large enough and the dynamics of them could be described by classical mechanics and the shape of the container is well known, it is possible to use the measured information in future to predict with more that 50% probability is the heat flux through the trapdoor from one part of the container to the other in each infinitesimal interval of time positive or negative (in the case when the trapdoor is open) and so create a temperature difference between two parts of the container.
In such case there is no violation of energy conservation law because the demon spends more energy for observation and calculation, but one could say that the information is stored inside the demon's memory storage.
My questions are following:
- Is it correct to say that the amount of useful energy that the demon could release using it's memory is equivalent to Helmholtz free energy in the system?
- Is it correct to say that the energy stored in the memory storage? Or it is better to formulate it in some more accurate words?
I'm interested in this thought experiment because I'm wonder what actually information is in physics and how is it related to energy and I will appreciate if one recommend some interesting reading about this topic.
P.S. The question is a bit related to this one Maxwell's Demon Constant (Information-Energy equivalence)